Erich L Kaltofen

Works (199)

Updated: October 2nd, 2025 05:11

2025 article

Early termination for sparse interpolation of polynomials in Chebyshev bases

Kaltofen, E. L., & Yang, Z.-H. (2025, September 4). Journal of Symbolic Computation, Vol. 134.

By: E. Kaltofen n  & Z. Yang*

author keywords: Chebyshev polynomials; Prony algorithm; Sparsity determination; Levinson-Durbin algorithm; Singular Toeplitz matrices; Heinig algorithm
topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation; Mathematical functions and polynomials; Digital Filter Design and Implementation; Numerical Methods and Algorithms
Sources: Web Of Science, NC State University Libraries
Added: September 29, 2025

2024 article

Encounters in Symbolic Computation: Ideas for the Ages

Kaltofen, E. L. (2024, July 15). PROCEEDINGS OF THE 2024 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2024, pp. 1–7.

By: E. Kaltofen* 

author keywords: History of polynomial factorization; computation of digits of pi; randomized linear algebra; Freivalds's algorithm; Wiedemann's algorithm
topics (OpenAlex): Cryptography and Data Security; Complexity and Algorithms in Graphs; semigroups and automata theory
Sources: Web Of Science, ORCID, NC State University Libraries
Added: September 23, 2024

2024 article

Sparse Polynomial Interpolation With Error Correction: Higher Error Capacity by Randomization

Kaltofen, E. L., & Yang, Z.-H. (2024, July 15). PROCEEDINGS OF THE 2024 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2024, pp. 264–273.

By: E. Kaltofen n  & Z. Yang *

author keywords: sparse model fitting; outlier error correction; orthogonal polynomial basis; Prony interpolation algorithm
topics (OpenAlex): Polynomial and algebraic computation; Complexity and Algorithms in Graphs; Computational Geometry and Mesh Generation
Sources: Web Of Science, ORCID, NC State University Libraries
Added: September 23, 2024

2022 article

Sparse Polynomial Hermite Interpolation

Kaltofen, E. L. (2022, July 4). PROCEEDINGS OF THE 2022 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2022, pp. 469–478.

By: E. Kaltofen* 

author keywords: model fitting; gradient data; measurement minimization
topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Cryptography and Residue Arithmetic
TL;DR: These algorithms generalize to multivariate polynomials, higher derivatives and sparsity with respect to Chebyshev polynomial bases, and have algorithms that can correct errors in the points by oversampling at a limited number of good values. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: September 11, 2023

2022 article

The GKR Protocol Revisited

Kaltofen, E. L. (2022, July 4). PROCEEDINGS OF THE 2022 INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, ISSAC 2022, pp. 177–186.

By: E. Kaltofen* 

author keywords: cloud computing; primality testing; proof-of-work certificate
topics (OpenAlex): Cryptography and Data Security; Complexity and Algorithms in Graphs; semigroups and automata theory
TL;DR: This protocol applies GKR recursively to the arising sumcheck problems on each level of the circuit whose values are verified, and deploys any of the prover-nearly-optimal versions of GKR on the constructed sorting/prefix circuits with log-depth wiring functions. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: September 11, 2023

2021 article

Computing Higher Polynomial Discriminants

Kaltofen, E. L. (2021, July 13). Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation.

By: E. Kaltofen n 

topics (OpenAlex): Polynomial and algebraic computation; Advanced Statistical Methods and Models; Advanced Data Processing Techniques
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Source: ORCID
Added: April 22, 2025

2021 article

Hermite Interpolation With Error Correction

Kaltofen, E. L., Pernet, C., & Yang, Z.-H. (2021, July 13). Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation.

By: E. Kaltofen n , C. Pernet * & Z. Yang *

topics (OpenAlex): Coding theory and cryptography; Advanced Wireless Communication Techniques; Error Correcting Code Techniques
Source: ORCID
Added: April 22, 2025

2020 article

A note on sparse polynomial interpolation in Dickson polynomial basis

Imamoglu, E., & Kaltofen, E. L. (2020, December 1). ACM Communications in Computer Algebra, Vol. 54, pp. 125–128.

By: E. Imamoglu * & E. Kaltofen n 

topics (OpenAlex): Digital Filter Design and Implementation; Low-power high-performance VLSI design; Coding theory and cryptography
TL;DR: The sparsity t≪ deg(f) with respect to the basis Pn has been exploited in interpolation algorithms that reconstruct the degree/coefficient expansion (δj, cj)1≤j≤t from values ai = f(γi) at the arguments x ← γi ∈ K. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: June 10, 2021

2020 article

Foreword

Kaltofen, E. L. (2020, April 22). Journal of Symbolic Computation, Vol. 105, pp. 1–3.

By: E. Kaltofen n 

Contributors: E. Kaltofen n 

topics (OpenAlex): Polynomial and algebraic computation
Sources: Web Of Science, ORCID, NC State University Libraries
Added: February 15, 2021

2020 article

Hermite Rational Function Interpolation with Error Correction

Kaltofen, E. L., Pernet, C., & Yang, Z.-H. (2020, January 1). Lecture Notes in Computer Science, pp. 335–357.

By: E. Kaltofen n , C. Pernet * & Z. Yang  n

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Numerical Methods and Algorithms
Source: ORCID
Added: April 22, 2025

2020 article

On computing the degree of a Chebyshev Polynomial from its value

Imamoglu, E., & Kaltofen, E. L. (2020, April 28). Journal of Symbolic Computation, Vol. 104, pp. 159–167.

By: E. Imamoglu * & E. Kaltofen n 

Contributors: E. Imamoglu * & E. Kaltofen n 

author keywords: Algorithms; Discrete logarithms; Chebyshev Polynomials; Interpolation in terms of the Chebyshev; Polynomials of the First Kind
topics (OpenAlex): Coding theory and cryptography; Cryptography and Residue Arithmetic; Polynomial and algebraic computation
TL;DR: An algorithm is given that can determine the Chebyshev degrees modulo such primes in bit complexity log ⁡ ( p ) O ( 1 ) times the squareroot of the largest prime factor of p − 1 (or p + 1 ). (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: January 19, 2021

2020 article

Sparse Interpolation With Errors in Chebyshev Basis Beyond Redundant-Block Decoding

Kaltofen, E. L., & Yang, Z.-H. (2020, September 30). IEEE Transactions on Information Theory, Vol. 67, pp. 232–243.

By: E. Kaltofen n  & Z. Yang  n

author keywords: Sparse polynomial interpolation; error correction; black box polynomial; list-decoding
topics (OpenAlex): Coding theory and cryptography; Numerical Methods and Algorithms; Polynomial and algebraic computation; Cryptography and Residue Arithmetic
TL;DR: Sparse interpolation algorithms for recovering a polynomial with LaTeX terms from inline-formula evaluations at distinct values for the variable with Chebyshev Basis, which return a list of valid sparse interpolants for the algorithm. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: January 19, 2021

2019 journal article

Computing Approximate Greatest Common Right Divisors of Differential Polynomials

Foundations of Computational Mathematics, 20(2), 331–366.

By: M. Giesbrecht*, J. Haraldson* & E. Kaltofen n 

Contributors: M. Giesbrecht*, J. Haraldson* & E. Kaltofen n 

author keywords: Symbolic-numeric computation; Approximate polynomial computation; Approximate GCD; Differential polynomials; Linear differential operators
topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Numerical methods for differential equations
TL;DR: The approximate greatest common right divisor problem (GCRD) of differential polynomials is introduced, as a non-commutative generalization of the well-studied approximate GCD problem. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 21, 2019

2019 article

Elimination-based certificates for triangular equivalence and rank profiles

Dumas, J.-G., Kaltofen, E., Lucas, D., & Pernet, C. (2019, July 16). Journal of Symbolic Computation, Vol. 98, pp. 246–269.

By: J. Dumas, E. Kaltofen n , D. Lucas & C. Pernet

Contributors: J. Dumas, E. Kaltofen n , D. Lucas & C. Pernet

author keywords: Interactive certificate; Rank profile; Linear algebra; Triangular equivalence; Verifiable computing
topics (OpenAlex): Complexity and Algorithms in Graphs; semigroups and automata theory; graph theory and CDMA systems
TL;DR: Novel certificates for triangular equivalence and rank profiles are given, enabling somebody to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a negligible overall overhead. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: December 30, 2019

2018 article

Sparse Polynomial Interpolation With Arbitrary Orthogonal Polynomial Bases

Imamoglu, E., Kaltofen, E. L., & Yang, Z. (2018, July 11). Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, pp. 223–230.

By: E. Imamoglu  n, E. Kaltofen n  & Z. Yang*

Contributors: E. Imamoglu  n, E. Kaltofen n  & Z. Yang*

topics (OpenAlex): Numerical Methods and Algorithms; Polynomial and algebraic computation; Coding theory and cryptography
TL;DR: These algorithms deterministically recover the sparse representation in the First, Second, Third and Fourth Kind Chebyshev representation from exactly t + B evaluations, and generalize to bases whose ChebysHEv recurrences have parametric scalars. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: February 25, 2019

2017 conference paper

Early Termination in Parametric Linear System Solving and Rational Function Vector Recovery with Error Correction

Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17, Part F129312, 237–244.

By: E. Kaltofen n , C. Pernet *, A. Storjohann * & C. Waddell n

Contributors: E. Kaltofen n , C. Pernet *, A. Storjohann * & C. Waddell n

topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation; Numerical Methods and Algorithms
TL;DR: An algorithm that given the same inputs uses possibly fewer evaluations to compute the solution and may recover it from fewer evaluations than generalized Welch/Berlekamp decoding, and develops a combined early termination algorithm. (via Semantic Scholar)
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UN Sustainable Development Goal Categories
Sources: Crossref, ORCID, NC State University Libraries
Added: July 21, 2019

2017 conference paper

Polynomial Time Interactive Proofs for Linear Algebra with Exponential Matrix Dimensions and Scalars Given by Polynomial Time Circuits

Proceedings of the 2017 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '17, Part F129312, 125–132.

By: J. Dumas *, E. Kaltofen n , G. Villard* & L. Zhi *

Contributors: J. Dumas *, E. Kaltofen n , G. Villard* & L. Zhi *

topics (OpenAlex): Complexity and Algorithms in Graphs; Polynomial and algebraic computation; Formal Methods in Verification
TL;DR: An interactive probabilistic proof protocol that certifies in (log N)O(1) arithmetic and Boolean operations for the verifier the determinant of an N x N matrix over a field whose entries a(i,j) are given by a single (log NO(1)-depth arithmetic circuit, which is polynomial time uniform. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 21, 2019

2016 article

Linear Time Interactive Certificates for the Minimal Polynomial and the Determinant of a Sparse Matrix

Dumas, J.-G., Kaltofen, E., Thomé, E., & Villard, G. (2016, July 19). Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, pp. 199–206.

By: J. Dumas *, E. Kaltofen n , E. Thomé * & G. Villard *

Contributors: J. Dumas *, E. Kaltofen n , E. Thomé * & G. Villard *

topics (OpenAlex): Cryptography and Data Security; Complexity and Algorithms in Graphs; Polynomial and algebraic computation
TL;DR: An algorithm is given that computes a certificate for the minimal polynomial of sparse or structured matrices over an abstract field, of sufficiently large cardinality, whose Monte Carlo verification complexity requires a single matrix-vector multiplication and a linear number of extra field operations. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2016 conference paper

Numerical Sparsity Determination and Early Termination

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16, 20-22-July-2016, 247–254.

By: Z. Hao *, E. Kaltofen n  & L. Zhi *

Contributors: Z. Hao *, E. Kaltofen n  & L. Zhi *

author keywords: Hankel matrix; Vandermonde matrix; sparse polynomial interpolation; condition number; early termination; sparse signal processing
topics (OpenAlex): Image and Signal Denoising Methods; Digital Filter Design and Implementation; Numerical Methods and Algorithms
TL;DR: An algorithm is given that can be used to compute the sparsity and estimate the minimal number of samples needed in numerical sparse interpolation and the early termination strategy of polynomial interpolation has been incorporated in the algorithm. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 21, 2019

2015 conference paper

Error-Correcting Sparse Interpolation in the Chebyshev Basis

Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15, 2015-June, 21–28.

By: A. Arnold* & E. Kaltofen n 

Contributors: A. Arnold* & E. Kaltofen n 

author keywords: sparse polynomial interpolation; Prony's algorithm; Chebyshev polynomials; Descartes' rule of signs; orthogonal basis; error-correcting code
topics (OpenAlex): Coding theory and cryptography; Cryptography and Residue Arithmetic; Polynomial and algebraic computation
TL;DR: The correctness of the list-decoder-based algorithm with a Descartes-rule-of-signs-like property for sparse polynomials in Chebyshev basis is proved and the many techniques for the sparse interpolation in power basis, for instance, supersparse (lacunary) interpolation over large finite fields, are made available to interpolation on Chebyshv basis. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 21, 2019

2015 conference paper

Foreword

ACM International Conference Proceeding Series, 10, v-vi. http://www.scopus.com/inward/record.url?eid=2-s2.0-84958074665&partnerID=MN8TOARS

By: J. Dumas, E. Kaltofen  & C. Pernet

Contributors: J. Dumas, E. Kaltofen  & C. Pernet

www.scopus.com
Source: ORCID
Added: April 22, 2025

2015 article

Numerical Linear System Solving with Parametric Entries by Error Correction

Boyer, B., & Kaltofen, E. L. (2015, February 5). ACM Communications in Computer Algebra, Vol. 48, pp. 103–105.

By: B. Boyer n & E. Kaltofen n 

Contributors: B. Boyer n & E. Kaltofen n 

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Matrix Theory and Algorithms
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
4. Quality Education (OpenAlex)
Source: ORCID
Added: April 22, 2025

2015 book

PASCO '15 Proceedings of the 2015 International Workshop on Parallel Symbolic Computation

New York, NY: Association for Computing Machinery.

Erich Kaltofen

Ed(s): J. Dumas, E. Kaltofen  & C. Pernet

Source: NC State University Libraries
Added: August 16, 2021

2015 article

Sparse multivariate function recovery with a small number of evaluations

Kaltofen, E. L., & Yang, Z. (2015, November 5). Journal of Symbolic Computation, Vol. 75, pp. 209–218.

By: E. Kaltofen n  & Z. Yang*

Contributors: E. Kaltofen n  & Z. Yang*

author keywords: Error correcting coding; Fault tolerance; Cauchy interpolation; Multivariate rational function model
topics (OpenAlex): Digital Filter Design and Implementation; Numerical Methods and Algorithms; Advanced Numerical Analysis Techniques
TL;DR: Here it is proved that T + O ( 1 ) evaluations at random points indeed suffice, thus providing the missing proof to Theorem 2.1 in Section 2 of the ISSAC 2014 paper. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2014 conference paper

Cleaning-up data for sparse model synthesis

Proceedings of the 2014 Symposium on Symbolic-Numeric Computation - SNC '14. Presented at the the 2014 Symposium.

By: E. Kaltofen n 

topics (OpenAlex): Model Reduction and Neural Networks; Tensor decomposition and applications; Matrix Theory and Algorithms
TL;DR: The pioneering creation of interpolation algorithms that can account for sparsity in the resulting multi-dimensional models are created, for example, by Zippel, Ben-Or and Tiwari and Kaltofen-Yang-Zhi. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 21, 2019

2014 conference paper

Essentially optimal interactive certificates in linear algebra

Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14, 146–153.

By: J. Dumas* & E. Kaltofen n 

Contributors: J. Dumas* & E. Kaltofen n 

topics (OpenAlex): Cryptography and Data Security; Complexity and Algorithms in Graphs; Formal Methods in Verification
TL;DR: All the authors' certificates are based on interactive verification protocols with the interaction removed by a Fiat-Shamir identification heuristic, and the validity of the verification procedure is subject to standard computational hardness assumptions from cryptography. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 21, 2019

2014 article

NSF funding opportunities for symbolic computation

Kaltofen, E., & Ovchinnikov, A. (2014, January 28). ACM Communications in Computer Algebra, Vol. 47, p. 84.

By: E. Kaltofen*  & A. Ovchinnikov

Contributors: E. Kaltofen*  & A. Ovchinnikov

topics (OpenAlex): Computability, Logic, AI Algorithms; Cellular Automata and Applications
Source: ORCID
Added: April 22, 2025

2014 conference paper

Numerical linear system solving with parametric entries by error correction

Proceedings of the 2014 Symposium on Symbolic-Numeric Computation - SNC '14, 33–38.

By: B. Boyer n & E. Kaltofen n 

Contributors: B. Boyer n & E. Kaltofen n 

topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation; Advanced Wireless Communication Techniques
TL;DR: The algorithm generalizes Welch/Berlekamp decoding of Reed/Solomon error correcting codes and their numeric floating point counterparts and gives an algorithm that computes the unique solution, which is a vector of rational functions, by evaluating the parameter u at distinct points. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 21, 2019

2014 chapter

Sparse Polynomial Interpolation by Variable Shift in the Presence of Noise and Outliers in the Evaluations

In Computer Mathematics (pp. 183–197).

By: B. Boyer n, M. Comer n & E. Kaltofen n 

topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Digital Filter Design and Implementation
TL;DR: By way of experiments, the techniques can recover approximate sparse shifted polynomial models, provided that there are few terms \(t\), few outliers and that the sparse shift is relatively small. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2014 conference paper

Sparse multivariate function recovery with a high error rate in the evaluations

Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14, 280–287.

By: E. Kaltofen n  & Z. Yang*

Contributors: E. Kaltofen n  & Z. Yang*

topics (OpenAlex): Digital Filter Design and Implementation; Numerical Methods and Algorithms; Advanced Image Processing Techniques
TL;DR: A different algorithm is presented that can interpolate a sparse multivariate rational function from evaluations where the error rate is 1/q for any q > 2, which the ISSAC 2013 algorithm could not handle. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 21, 2019

2014 conference paper

Sparse polynomial interpolation codes and their decoding beyond half the minimum distance

Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14, 272–279.

By: E. Kaltofen n  & C. Pernet*

Contributors: E. Kaltofen n  & C. Pernet*

topics (OpenAlex): Coding theory and cryptography; Error Correcting Code Techniques; Advanced Wireless Communication Techniques
TL;DR: A new polynomial-time list decoding algorithm uses sub-sequences of the received evaluations indexed by an arithmetic progression, allowing the decoding for a larger radius, that is, more errors in the evaluations while returning a list of candidate sparse polynomials. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 21, 2019

2014 chapter

Symbolic Computation and Complexity Theory Transcript of My Talk

In Computer Mathematics (pp. 3–7).

By: E. Kaltofen n 

topics (OpenAlex): Computability, Logic, AI Algorithms; Algorithms and Data Compression; semigroups and automata theory
TL;DR: I gave talks at the conference Alan Turing’s Heritage: Logic, Computation & Complexity in Lyon, France, and at the Tenth Asian Symposium on Computer Mathematics (ASCM) in Beijing, China, on the complexity theoretic hardness of many problems that the discipline of symbolic computation tackles. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2013 article

A fraction free Matrix Berlekamp/Massey algorithm

Kaltofen, E., & Yuhasz, G. (2013, August 13). Linear Algebra and Its Applications, Vol. 439, pp. 2515–2526.

By: E. Kaltofen n  & G. Yuhasz n

Contributors: E. Kaltofen n  & G. Yuhasz n

author keywords: Exact division; Linear recurrences; Matrix recurrences; Block Hankel systems; Block Toeplitz systems; Integer sequences
topics (OpenAlex): Coding theory and cryptography; Matrix Theory and Algorithms; Advanced Wireless Communication Techniques
TL;DR: This new scalar algorithm has smaller intermediate values than the known fraction free Berlekamp/Massey algorithm and performs all operations in the integral domain, so all divisions performed are exact. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2013 chapter

Factorization of multivariate polynomials

In G. L. Mullen & D. Panario (Eds.), Handbook of Finite Fields (pp. 382–392). Boca Raton, Florida: CRC Press, Taylor & Francis Group.

By: E. Kaltofen  & G. Lecerf

Ed(s): G. Mullen & D. Panario

Source: NC State University Libraries
Added: March 26, 2022

2013 article

On the matrix berlekamp-massey algorithm

Kaltofen, E., & Yuhasz, G. (2013, September 1). ACM Transactions on Algorithms, Vol. 9.

By: E. Kaltofen n  & G. Yuhasz n

Contributors: E. Kaltofen n  & G. Yuhasz n

author keywords: Linear generated sequences; matrix polynomials; minimal generators; vector Berlekamp/Massey algorithm; multivariable linear control
topics (OpenAlex): Coding theory and cryptography; Advanced Wireless Communication Techniques; Matrix Theory and Algorithms
TL;DR: This work analyzes the Matrix Berlekamp/Massey algorithm and gives new proofs of correctness and complexity for the algorithm, which is based on self-contained loop invariants and includes an explicit termination criterion for a given determinantal degree bound of the minimal matrix generator. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2013 conference paper

Sparse multivariate function recovery from values with noise and outlier errors

Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation - ISSAC '13, 219–226.

By: E. Kaltofen n  & Z. Yang*

Contributors: E. Kaltofen n  & Z. Yang*

topics (OpenAlex): Digital Filter Design and Implementation; Sparse and Compressive Sensing Techniques; Numerical Methods and Algorithms
TL;DR: This work gives a different univariate solution based on structured linear algebra that yields a stable decoder with floating point arithmetic that can build a sparse model from a number of evaluations that is linear in the sparsity of the model. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 27, 2019

2012 conference paper

Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12, 195–202.

By: F. Guo *, E. Kaltofen n  & L. Zhi *

Contributors: F. Guo *, E. Kaltofen n  & L. Zhi *

topics (OpenAlex): Advanced Optimization Algorithms Research; Numerical Methods and Algorithms; Polynomial and algebraic computation
TL;DR: The algorithm is demonstrated by computing certificates of impossibilities for an arbitrary sum-of-squares denominator of degree 2 and 4 for some symmetric sextics in 4 and 5 variables, respectively. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 27, 2019

2012 conference paper

Fast estimates of Hankel matrix condition numbers and numeric sparse interpolation

Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation - SNC '11, 130–136.

By: E. Kaltofen n , W. Lee * & Z. Yang *

Contributors: E. Kaltofen n , W. Lee * & Z. Yang *

topics (OpenAlex): Mathematical functions and polynomials; Matrix Theory and Algorithms; Mathematical Analysis and Transform Methods
Sources: Crossref, ORCID, NC State University Libraries
Added: July 27, 2019

2012 conference paper

Sparse polynomial interpolation and Berlekamp/Massey algorithms that correct outlier errors in input values

Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation - ISSAC '12, 138–145.

By: M. Comer n, E. Kaltofen n  & C. Pernet *

Contributors: M. Comer n, E. Kaltofen n  & C. Pernet *

topics (OpenAlex): Coding theory and cryptography; Numerical Methods and Algorithms; Polynomial and algebraic computation
TL;DR: The Majority Rule Berlekamp/Massey algorithm, which can recover the unique minimal linear generator of degree <i>t</i> when given bounds and the Majority Rule algorithm yields a unique sparse interpolant for the first problem. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 27, 2019

2011 journal article

Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients

Journal of Symbolic Computation, 47(1), 1–15.

By: E. Kaltofen n , B. Li *, Z. Yang* & L. Zhi *

Contributors: E. Kaltofen n , B. Li *, Z. Yang* & L. Zhi *

author keywords: Semidefinite programming; Sum-of-squares; Validated output; Hybrid method
topics (OpenAlex): Polynomial and algebraic computation; Advanced Optimization Algorithms Research; Numerical Methods and Algorithms
TL;DR: This work presents a hybrid symbolic-numeric algorithm for certifying a polynomial or rational function with rational coefficients to be non-negative for all real values of the variables by computing a representation for it as a fraction of twoPolynomial sum-of-squares (SOS) with rational coefficient. (via Semantic Scholar)
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UN Sustainable Development Goal Categories
4. Quality Education (OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 27, 2019

2011 article

On the Berlekamp/Massey algorithm and counting singular Hankel matrices over a finite field

Comer, M. T., & Kaltofen, E. L. (2011, September 17). Journal of Symbolic Computation, Vol. 47, pp. 480–491.

By: M. Comer n & E. Kaltofen n 

Contributors: M. Comer n & E. Kaltofen n 

author keywords: Toeplitz matrix; Hankel matrix; Block matrix; Finite field; Singularity counts; Fixed entry; Berlekamp/Massey algorithm
topics (OpenAlex): Coding theory and cryptography; graph theory and CDMA systems; DNA and Biological Computing
TL;DR: An explicit count for the number of singular nxn Hankel (Toeplitz) matrices whose entries range over a finite field with q elements is derived by observing the execution of the Berlekamp/Massey algorithm on its elements. (via Semantic Scholar)
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Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2011 conference paper

Quadratic-time certificates in linear algebra

Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11, 171–176.

By: E. Kaltofen n , M. Nehring n & B. Saunders*

Contributors: E. Kaltofen n , M. Nehring n & B. Saunders*

topics (OpenAlex): Polynomial and algebraic computation; Complexity and Algorithms in Graphs; Advanced Combinatorial Mathematics
Sources: Crossref, ORCID, NC State University Libraries
Added: August 18, 2019

2011 article

Special Issue on Symbolic and Algebraic Computation Foundations, Algorithmics and Applications: ISSAC 2009

Johnson, J. R., Kaltofen, E., & Park, H. (2011, December 22). Journal of Symbolic Computation, Vol. 47, p. 751.

By: J. Johnson *, E. Kaltofen n  & H. Park *

Contributors: J. Johnson *, E. Kaltofen n  & H. Park *

topics (OpenAlex): Polynomial and algebraic computation; Computability, Logic, AI Algorithms; Numerical Methods and Algorithms
TL;DR: The papers included in the Special Issue cover investigations on computational homology, fast algorithms for computing order bases of matrices of power series, fast arithmetic in Artin–Schreier towers with applications to elliptic curves, polynomial system solving, and quantifier elimination. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2011 conference paper

Supersparse black box rational function interpolation

Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11, 177–185.

By: E. Kaltofen n  & M. Nehring n

Contributors: E. Kaltofen n  & M. Nehring n

topics (OpenAlex): Tensor decomposition and applications; Polynomial and algebraic computation; Mathematical Analysis and Transform Methods
TL;DR: A method for interpolating a supersparse blackbox rational function with rational coefficients, for example, a ratio of binomials or trinomials with very high degree, which is very effective for rational functions with a small number of non-zero terms, but it quickly becomes ineffective for a high number of terms. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 27, 2019

2011 article

Symmetric Determinantal Representation of Weakly-Skew Circuits

Grenet, B., Kaltofen, E. L., Koiran, P., & Portier, N. (2011, January 1). (C. Dürr & T. Schwentick, Eds.). DROPS (Schloss Dagstuhl – Leibniz Center for Informatics), Vol. 9, pp. 543–554.

By: B. Grenet *, E. Kaltofen n , P. Koiran * & N. Portier*

Contributors: B. Grenet *, E. Kaltofen n , P. Koiran * & N. Portier*

Ed(s): C. Dürr & T. Schwentick

topics (OpenAlex): Polynomial and algebraic computation; Formal Methods in Verification; Commutative Algebra and Its Applications
Sources: ORCID, NC State University Libraries
Added: April 22, 2025

2011 other

Symmetric determinantal representation of formulas and weakly skew circuits

By: B. Grenet *, E. Kaltofen* , P. Koiran * & N. Portier*

topics (OpenAlex): Polynomial and algebraic computation; Advanced Combinatorial Mathematics; Commutative Algebra and Its Applications
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2011 conference paper

Symmetric determinantal representation of weakly skew circuits

In C. Dürr & T. Schwentick (Eds.), Proceedings of the Symposium on Theoretical Aspects of Computer Science (STACS 2011) (pp. 543–554). Germany.

By: B. Grenet, E. Kaltofen , P. Koiran & N. Portier

Ed(s): C. Dürr & T. Schwentick

Event: Symposium on Theoretical Aspects of Computer Science (STACS 2011) at Dortmund, Germany

Source: NC State University Libraries
Added: March 26, 2022

2011 chapter

The “Seven Dwarfs” of Symbolic Computation

In Texts & Monographs in Symbolic Computation (pp. 95–104).

By: E. Kaltofen n 

topics (OpenAlex): Polynomial and algebraic computation; Algorithms and Data Compression; Coding theory and cryptography
TL;DR: The Seven Dwarfs of Symbolic Computation, which are sequential and parallel algorithmic methods that today carry a great majority of all exact and hybrid symbolic compute cycles, are presented. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: July 27, 2019

2011 article

What is Hybrid Symbolic-Numeric Computation?

Kaltofen, E. (2011, September 1). Proceedings - 13th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing, SYNASC 2011, p. 11.

By: E. Kaltofen n 

Contributors: E. Kaltofen n 

topics (OpenAlex): Polynomial and algebraic computation; Matrix Theory and Algorithms; Numerical Methods and Algorithms
Source: ORCID
Added: April 22, 2025

2010 conference paper

Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of Seidenberg's method

Proceedings of the 2010 International Symposium on Symbolic and Algebraic Computation - ISSAC '10, 227–234.

By: S. Hutton n, E. Kaltofen n  & L. Zhi *

Contributors: S. Hutton n, E. Kaltofen n  & L. Zhi *

topics (OpenAlex): Numerical Methods and Algorithms; Advanced Optimization Algorithms Research; Matrix Theory and Algorithms
TL;DR: Sums-of-squares rational lower bound certificates for the radius of semidefiniteness provide a new approach to solving Seidenberg's problem, especially when the coefficients are numeric. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
10. Reduced Inequalities (OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 18, 2019

2010 article

Efficiently Certifying Non-Integer Powers

Kaltofen, E., & Lavin, M. (2010, August 7). Computational Complexity, Vol. 19, pp. 355–366.

By: E. Kaltofen n  & M. Lavin n

Contributors: E. Kaltofen n  & M. Lavin n

author keywords: Integer roots; integer powers; linear-time algorithm; bit complexity; Chebotarev density theorem
topics (OpenAlex): Analytic Number Theory Research; Limits and Structures in Graph Theory
TL;DR: A randomized algorithm that, given an integer a, produces a certificate that the integer is not a pure power of an integer in expected (log a)1+o(1) bit operations under the assumption of the Generalized Riemann Hypothesis is described. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2010 conference paper

Fifteen years after DSC and WLSS2 what parallel computations I do today

Proceedings of the 4th International Workshop on Parallel and Symbolic Computation - PASCO '10, 10–17.

By: E. Kaltofen n 

Contributors: E. Kaltofen n 

topics (OpenAlex): Complexity and Algorithms in Graphs; Algorithms and Data Compression; Parallel Computing and Optimization Techniques
TL;DR: The paradigm of interactive symbolic supercomputing is proposed, a symbolic computation environment analog of the STAR-P Matlab platform, and multivariate sparse polynomial parallel interpolation constitutes a keystone operation, for which a new algorithm is presented. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 18, 2019

2010 report

The Role of Symbolic, Numeric and Algebraic Computation in Cyber-Enabled Discovery and Innovation (CDI)

In Future Directions of Symbolic Computation Research And Their Applications to the Domain Sciences. University of Rhode Island.

By: E. Kaltofen 

Source: NC State University Libraries
Added: March 26, 2022

2009 conference paper

A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions

Proceedings of the 2009 conference on Symbolic numeric computation - SNC '09, 65–69.

By: E. Kaltofen n , Z. Yang * & L. Zhi *

Contributors: E. Kaltofen n , Z. Yang * & L. Zhi *

topics (OpenAlex): Advanced Optimization Algorithms Research; Matrix Theory and Algorithms; Polynomial and algebraic computation
TL;DR: Here a hybrid symbolic-numerical algorithm is applied for certifying that 4 polynomials can be written as an exact fraction of two polynomial sums-of-squares (SOS) with rational coefficients. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 18, 2019

2009 conference paper

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC: Foreword

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC. http://www.scopus.com/inward/record.url?eid=2-s2.0-77950420782&partnerID=MN8TOARS

By: J. Johnson, E. Kaltofen , J. May & H. Park

Contributors: J. Johnson, E. Kaltofen , J. May & H. Park

www.scopus.com
Source: ORCID
Added: April 22, 2025

2008 conference paper

Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08, 155–163.

By: E. Kaltofen n , B. Li *, Z. Yang n & L. Zhi *

Contributors: E. Kaltofen n , B. Li *, Z. Yang n & L. Zhi *

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Advanced Optimization Algorithms Research
TL;DR: This work generalizes the technique by Peyrl and Parillo to computing lower bound certificates for several well-known factorization problems in hybrid symbolic-numeric computation and certifies accurate rational lower bounds near the irrational global optima. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 18, 2019

2008 conference paper

Expressing a fraction of two determinants as a determinant

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08, 141–146.

By: E. Kaltofen n  & P. Koiran *

Contributors: E. Kaltofen n  & P. Koiran *

topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation; graph theory and CDMA systems
TL;DR: The problem was motivated by resultant formulas derived from Chow forms and shows that divisions can be removed from formulas that compute polynomials in the input variables over a sufficiently large field within polynomial formula size growth. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 18, 2019

2007 article

Approximate factorization of multivariate polynomials using singular value decomposition

Kaltofen, E., May, J. P., Yang, Z., & Zhi, L. (2007, December 5). Journal of Symbolic Computation, Vol. 43, pp. 359–376.

By: E. Kaltofen n , J. May*, Z. Yang* & L. Zhi *

Contributors: E. Kaltofen n , J. May*, Z. Yang* & L. Zhi *

author keywords: multivariate polynomial factorization; approximate factorization; singular value decomposition; numerical algebra; Gauss-Newton optimization
topics (OpenAlex): Numerical Methods and Algorithms; Digital Filter Design and Implementation; Polynomial and algebraic computation
TL;DR: These algorithms are based on a generalization of the differential forms introduced by W. Ruppert and S. Gao to many variables, and use singular value decomposition or structured total least squares approximation and Gauss-Newton optimization to numerically compute the approximate multivariate factors. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2007 article

Computer Algebra Systems

(2007, August 14).

Erich Kaltofen

topics (OpenAlex): Educational Technology and Assessment
Sources: NC State University Libraries, NC State University Libraries
Added: August 6, 2018

2007 journal article

Irreducible polynomials and barker sequences

ACM Communications in Computer Algebra, 41(4), 118.

By: P. Borwein*, E. Kaltofen n  & M. Mossinghoff *

topics (OpenAlex): Coding theory and cryptography; Cryptography and Residue Arithmetic; graph theory and CDMA systems
TL;DR: It is shown that in this case the problem can in fact be reduced to a question of irreducibility for a certain family of univariate polynomials, and it is proved that the polynmials in question are always reducible modulo <i>p</i>, for every prime. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 18, 2019

2007 article

Lower bounds for approximate factorizations via semidefinite programming

Kaltofen, E., Li, B., Sivaramakrishnan, K., Yang, Z., & Zhi, L. (2007, July 25). SNC'07 - Proceedings of the 2007 International Workshop on Symbolic-Numeric Computation, pp. 203–204.

By: E. Kaltofen n , B. Li *, K. Sivaramakrishnan n, Z. Yang n & L. Zhi *

Contributors: E. Kaltofen n , B. Li *, K. Sivaramakrishnan n, Z. Yang n & L. Zhi *

topics (OpenAlex): Advanced Optimization Algorithms Research; Polynomial and algebraic computation; Numerical Methods and Algorithms
Source: ORCID
Added: April 22, 2025

2007 conference paper

Lower bounds for approximate factorizations via semidefinite programming

In J. Verschelde & S. M. Watt (Eds.), Proceedings of the 2007 International Workshop on Symbolic-Numeric Computation (SNC '07) (pp. 203–204). New York, NY: ACM Press.

By: E. Kaltofen , B. Li, K. Sivaramakrishnan, Z. Yang & L. Zhi

Ed(s): J. Verschelde & S. Watt

Event: International Workshop on Symbolic-Numeric Computation at London, Ontario, Canada on July 25-27, 2007

Source: NC State University Libraries
Added: March 26, 2022

2007 article

On exact and approximate interpolation of sparse rational functions

Kaltofen, E., & Yang, Z. (2007, July 29). Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, pp. 203–210.

By: E. Kaltofen n  & Z. Yang n

Contributors: E. Kaltofen n  & Z. Yang n

topics (OpenAlex): Advanced Numerical Analysis Techniques; Digital Filter Design and Implementation; Numerical Methods and Algorithms
TL;DR: Five new algorithms for sparse rational function interpolation algorithm in the hybrid symbolic-numeric setting when the black box for the function returns real and complex values with noise are presented and analyzed. (via Semantic Scholar)
Sources: NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018

2007 article

On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms

Kaltofen, E., Yang, Z., & Zhi, L. (2007, July 25). SNC'07 - Proceedings of the 2007 International Workshop on Symbolic-Numeric Computation, pp. 11–17.

By: E. Kaltofen n , Z. Yang n & L. Zhi *

Contributors: E. Kaltofen n , Z. Yang n & L. Zhi *

topics (OpenAlex): Matrix Theory and Algorithms; Markov Chains and Monte Carlo Methods; Random Matrices and Applications
Sources: ORCID, NC State University Libraries
Added: April 22, 2025

2007 conference paper

On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms

International Workshop on Symbolic-Numeric Computation: Proceedings. New York: ACM Press.

By: E. Kaltofen , Z. Yang & L. Zhi

Source: NC State University Libraries
Added: August 6, 2018

2007 chapter

Structured Low Rank Approximation of a Sylvester Matrix

In Trends in Mathematics (Vol. 41, pp. 69–83).

By: E. Kaltofen n , Z. Yang* & L. Zhi *

Contributors: E. Kaltofen n , Z. Yang* & L. Zhi *

author keywords: Sylvester matrix; approximate greatest common divisor; structured total least norm; hybrid symbolic/numeric algorithm
topics (OpenAlex): Statistical and numerical algorithms; Numerical Methods and Algorithms; Geophysics and Gravity Measurements
TL;DR: This work presents iterative algorithms that compute an approximate GCD and that can certify an approximate ∈-GCD when a tolerance ∈ is given on input and demonstrates the practical performance of these algorithms on a diverse set of univariate pairs of polynomials. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 18, 2019

2006 conference paper

Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials

Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06, 2006, 169–176.

By: E. Kaltofen* , Z. Yang* & L. Zhi *

Contributors: E. Kaltofen* , Z. Yang* & L. Zhi *

topics (OpenAlex): Numerical Methods and Algorithms; Polynomial and algebraic computation; Matrix Theory and Algorithms
TL;DR: This work presents an algorithm based on a version of the structured total least norm (STLN) method and demonstrates that the algorithm in practice computes globally minimal approximations on a diverse set of benchmark polynomials. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 18, 2019

2006 conference paper

Challenges in Symbolic Computation Software, number 06271

In Dagstuhl Seminar Proceedings. Germany: Schloss Dagstuhl.

Erich Kaltofen

Ed(s): W. Decker, M. Dewar, E. Kaltofen  & S. Watt

Event: Internationales Begegnungs- und Forschungszentrum für Informatik (IBFI) at Schloss Dagstuhl

Source: NC State University Libraries
Added: March 26, 2022

2006 conference paper

Finding small degree factors of multivariate supersparse (lacunary) polynomials over algebraic number fields

Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06, 2006, 162–168.

By: E. Kaltofen*  & P. Koiran *

Contributors: E. Kaltofen*  & P. Koiran *

topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation; Cryptography and Residue Arithmetic
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

2006 conference paper

Hybrid symbolic-numeric computation

Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06, 2006, 7.

By: E. Kaltofen*  & L. Zhi *

Contributors: E. Kaltofen*  & L. Zhi *

topics (OpenAlex): Numerical Methods and Algorithms; Polynomial and algebraic computation; Advanced Numerical Analysis Techniques
TL;DR: The focus of the tutorial is on how to formulate several approximate symbolic computation problems as numerical problems in linear algebra and optimization and on software that realizes their solutions. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

2005 chapter

A note on the Risch differential equation

In J. Fitch (Ed.), EUROSAM 84: Vol. 174 LNCS (pp. 359–366).

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

Ed(s): J. Fitch

topics (OpenAlex): Polynomial and algebraic computation; Advanced Combinatorial Mathematics; Mathematics and Applications
TL;DR: This paper relates to the technique of integrating a function in a purely transcendental regular elementary Liouville extension by prescribing degree bounds for the transcendentals and then solving linear systems over the constants. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

2005 chapter

Effective Hilbert irreducibility

In EUROSAM 84: Vol. 174 LNCS (pp. 277–284).

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Cryptography and Data Security; Complexity and Algorithms in Graphs; Polynomial and algebraic computation
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

2005 chapter

Explicit construction of the hilbert class fields of imaginary quadratic fields with class numbers 7 and 11

In J. Fitch (Ed.), EUROSAM 84: Vol. 174 LNCS (pp. 310–320).

By: E. Kaltofen*  & N. Yui*

Contributors: E. Kaltofen*  & N. Yui*

Ed(s): J. Fitch

topics (OpenAlex): Algebraic Geometry and Number Theory; Homotopy and Cohomology in Algebraic Topology; Advanced Algebra and Geometry
TL;DR: This paper gives an explicit construction of the Hilbert class fields of some imaginary quadratic fields with class numbers 7 and 11 by explicitly evaluating the elliptic modular j -invariant at each representative of the ideal class of an imaginary Quadratic field, and forming the class equation. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

2005 conference paper

Generic matrix multiplication and memory management in linBox

Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05, 2005, 216–223.

By: E. Kaltofen n , D. Morozov * & G. Yuhasz n

Contributors: E. Kaltofen n , D. Morozov * & G. Yuhasz n

topics (OpenAlex): Parallel Computing and Optimization Techniques; Distributed and Parallel Computing Systems; Matrix Theory and Algorithms
TL;DR: An interface mechanism that allows incorporation of external components with native memory management such as garbage collection into LinBox and an implementation of the interface based on SACLIB's field arithmetic procedures is presented. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

2005 article

On the complexity of computing determinants

Kaltofen, E., & Villard, G. (2005, February 1). Computational Complexity, Vol. 13, pp. 91–130.

By: E. Kaltofen n  & G. Villard *

Contributors: E. Kaltofen n  & G. Villard *

author keywords: integer matrix; matrix determinant; characteristic polynomial; Smith normal form; bit complexity; division-free complexity; randomized algorithm; multivariable control theory; realization; matrix sequence; block Wiedemann algorithm; block Lanczos algorithm
topics (OpenAlex): Coding theory and cryptography; graph theory and CDMA systems; Polynomial and algebraic computation
TL;DR: New baby steps/giant steps algorithms of asymptotically fast running time for dense matrix problems that deterministically compute the determinant, characteristic polynomial and adjoint of A with n3.2+o(1) and O(n2.697263) ring additions, subtractions and multiplications are presented. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2005 conference paper

On the complexity of factoring bivariate supersparse (Lacunary) polynomials

Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05, 2005, 208–215.

By: E. Kaltofen n  & P. Koiran *

Contributors: E. Kaltofen n  & P. Koiran *

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Cryptography and Residue Arithmetic
TL;DR: Algorithms that compute linear and quadratic factors of supersparse (lacunary) bivariate polynomials over the rational numbers in polynomial-time in the input size and it is shown that the problem of determining the irreducibility of a supersparse bivariatePolynomial over a large finite field of any characteristic is co-NP-hard via randomized reductions. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

2005 chapter

Polynomial factorization 1987–1991

In Lecture Notes in Computer Science: Vol. 583. LATIN '92 (pp. 294–313).

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Cryptography and Data Security; Complexity and Algorithms in Graphs
TL;DR: This article discusses important developments of the past five years in factorization and discusses the “classical univariate problems” of factoring a polynomial. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

2005 conference paper

Process scheduling in DSC and the large sparse linear systems challenge

Design and Implementation of Symbolic Computation Systems (DISCO 1993), 722 LNCS, 66–80.

By: A. Diaz *, M. Hitz*, E. Kaltofen* , A. Lobo* & T. Valente *

Contributors: A. Diaz *, M. Hitz*, E. Kaltofen* , A. Lobo* & T. Valent *

topics (OpenAlex): Coding theory and cryptography; Cryptography and Residue Arithmetic; Low-power high-performance VLSI design
TL;DR: An algorithm is implemented that can prove a number of more than 1,000 decimal digits prime in about 2 months elapsed time on some 20 computers and a parallel version of a sparse linear system solver is used to compute the solution of sparse linear systems over finite fields. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

2004 chapter

Algebraic algorithms

In Computer Science Handbook, Second Edition (pp. 8–1-8–24). http://www.scopus.com/inward/record.url?eid=2-s2.0-85056559853&partnerID=MN8TOARS

Contributors: A. Diaz, E. Kaltófen  & V. Pan

www.scopus.com
Source: ORCID
Added: April 22, 2025

2004 conference paper

Approximate factorization of multivariate polynomials via differential equations

Proceedings of the 2004 international symposium on Symbolic and algebraic computation - ISSAC '04, 167–174.

By: S. Gao *, E. Kaltofen n , J. May  n, Z. Yang* & L. Zhi *

Contributors: S. Gao *, E. Kaltofen n , J. May  n, Z. Yang* & L. Zhi *

topics (OpenAlex): Polynomial and algebraic computation; Cryptography and Residue Arithmetic; Numerical Methods and Algorithms
TL;DR: It is demonstrated on a significant body of experimental data that the algorithm is practical and can find factorizable polynomials within a distance that is about the same in relative magnitude as the input error, even when the relative error in the input is substantial. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

2004 article

Deterministic distinct-degree factorization of polynomials over finite fields

Gao, S., Kaltofen, E., & Lauder, A. G. B. (2004, August 24). Journal of Symbolic Computation, Vol. 38, pp. 1461–1470.

By: S. Gao *, E. Kaltofen n  & A. Lauder*

Contributors: S. Gao *, E. Kaltofen n  & A. Lauder*

author keywords: multivariate polynomial; deterministic algorithm; distinct-degree factorization
topics (OpenAlex): Coding theory and cryptography; Cryptography and Residue Arithmetic; Cryptographic Implementations and Security
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2004 journal article

Early termination in Shoup's algorithm for the minimum polynomial of an algebraic

By: W. Eberly & E. Kaltofen 

Source: NC State University Libraries
Added: March 26, 2022

2003 chapter

Absolute factorization of polynomials

In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), Computer Algebra Handbook (p. 26). Heidelberg, Germany: Springer Verlag.

By: E. Kaltofen 

Ed(s): J. Grabmeier, E. Kaltofen  & V. Weispfenning

Source: NC State University Libraries
Added: December 5, 2020

2003 article

Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases

Giesbrecht, M., Kaltofen, E., & Lee, W.-shin. (2003, July 16). Journal of Symbolic Computation, Vol. 36, pp. 401–424.

By: M. Giesbrecht*, E. Kaltofen n  & W. Lee *

Contributors: M. Giesbrecht*, E. Kaltofen n  & W. Lee *

author keywords: sparse shifts; early termination; sparse polynomial; sparse interpolation; Chebyshev basis; Pochhammer basis
topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Coding theory and cryptography
TL;DR: These algorithms are based on the early termination version of sparse interpolation algorithms: for a symbolic set of interpolation points, a sparsest shift must be a root of the first possible zero discrepancy that can be used as the earlytermination test. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2003 book

Computer Algebra Handbook

(J. Grabmeier, E. Kaltofen, & V. Weispfenning, Eds.). Heidelberg, Germany: Springer Verlag.

By: J. Grabmeier & V. Weispfenning

Ed(s): J. Grabmeier, E. Kaltofen  & V. Weispfenning

Source: NC State University Libraries
Added: March 26, 2022

2003 chapter

Computer algebra - impact on research

In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), Computer Algebra Handbook (pp. 4–6). Heidelberg, Germany: Springer Verlag.

By: E. Kaltofen  & V. Weispfenning

Ed(s): J. Grabmeier, E. Kaltofen  & V. Weispfenning

Source: NC State University Libraries
Added: December 5, 2020

2003 article

Computing the sign or the value of the determinant of an integer matrix, a complexity survey

Kaltofen, E., & Villard, G. (2003, October 30). Journal of Computational and Applied Mathematics, Vol. 162, pp. 133–146.

By: E. Kaltofen n  & G. Villard *

Contributors: E. Kaltofen n  & G. Villard *

author keywords: determinant; bit-complexity; integer matrix; approximate computation; exact computation; randomized algorithms
topics (OpenAlex): Polynomial and algebraic computation; graph theory and CDMA systems; Matrix Theory and Algorithms
TL;DR: This work surveys the complexity of existing methods to solve problems when the input is an n × n matrix A with integer entries and studies the bit-complexities of the algorithms asymptotically in n and the norm of A. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2003 article

Early termination in sparse interpolation algorithms

Kaltofen, E., & Lee, W.-shin. (2003, July 16). Journal of Symbolic Computation, Vol. 36, pp. 365–400.

By: E. Kaltofen n  & W. Lee *

Contributors: E. Kaltofen n  & W. Lee *

author keywords: early termination; sparse polynomial; black box polynomial; interpolation; sparse interpolation; randomized algorithm
topics (OpenAlex): Advanced Combinatorial Mathematics; Polynomial and algebraic computation; Data Management and Algorithms
TL;DR: Based on early termination, racing algorithms execute simultaneously dense and sparse algorithms that can be embedded as the univariate interpolation substep within Zippel's multivariate method. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2003 chapter

FoxBox and other blackbox systems

In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), Computer Algebra Handbook (pp. 383–385). Heidelberg, Germany: Springer Verlag.

By: E. Kaltofen 

Ed(s): J. Grabmeier, E. Kaltofen  & V. Weispfenning

Source: NC State University Libraries
Added: December 5, 2020

2003 chapter

Hybrid methods

In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), Computer Algebra Handbook (pp. 112–125). Heidelberg, Germany: Springer Verlag.

By: M. Corless, E. Kaltofen  & S. Watt

Ed(s): J. Grabmeier, E. Kaltofen  & V. Weispfenning

Source: NC State University Libraries
Added: December 5, 2020

2003 chapter

Linear systems

In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), Computer algebra handbook: foundations, applications, systems (pp. 36–38). Heidelberg, Germany: Springer Verlag.

By: E. Kaltofen  & B. Saunders

Ed(s): J. Grabmeier, E. Kaltofen  & V. Weispfenning

Source: NC State University Libraries
Added: December 5, 2020

2003 conference paper

On approximate irreducibility of polynomials in several variables

Proceedings of the 2003 international symposium on Symbolic and algebraic computation - ISSAC '03, 161–168.

By: E. Kaltofen n  & J. May  n

Contributors: E. Kaltofen n  & J. May  n

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Coding theory and cryptography
TL;DR: Using an absolute irreducibility criterion due to Ruppert, this work is able to find useful separation bounds, in several norms, for bivariate polynomials, and derive new, more effective Noether forms for polynmials of arbitrarily many variables. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

2003 conference paper

Polynomial factorization

Proceedings of the 2003 international symposium on Symbolic and algebraic computation - ISSAC '03. Presented at the the 2003 international symposium.

By: E. Kaltofen n 

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Commutative Algebra and Its Applications
TL;DR: The baby steps/giant steps technique and fast distinct and equaldegree factorization implementations have, at last, yielded in themid 1990s theoretical and practical improvements over the originalunivariate Berlekamp algorithm for coefficients in finite fields. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

2002 conference paper

'Using Maple to grade Maple' assessment software from North Carolina State University

Proceedings 2002 Maple Workshop. Waterloo, Canada: Waterloo Maple Inc. With Dmitriy Morozov, John May and William Turner.

By: E. Kaltofen , M. McLean & L. Norris

Source: NC State University Libraries
Added: March 26, 2022

2002 conference paper

Algorithms for computing the sparsest shifts of polynomials via the Berlekamp/Massey algorithm

Proceedings of the 2002 international symposium on Symbolic and algebraic computation - ISSAC '02, 101–108.

By: M. Giesbrecht*, E. Kaltofen n  & W. Lee *

Contributors: M. Giesbrecht*, E. Kaltofen n  & W. Lee *

topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation; Matrix Theory and Algorithms
TL;DR: A fraction-free version of the Berlekamp/Massey algorithm is given, which does not require rational numbers or functions and GCD operations on the arising numerators and denominators and is more efficient than the classical extended Euclidean algorithm. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: May 18, 2021

2002 conference paper

An output-sensitive variant of the baby steps/giant steps determinant algorithm

Proceedings of the 2002 international symposium on Symbolic and algebraic computation - ISSAC '02, 138–144.

By: E. Kaltofen n 

Contributors: E. Kaltofen n 

topics (OpenAlex): Coding theory and cryptography; Algorithms and Data Compression; Polynomial and algebraic computation
TL;DR: An algorithm in [15], which in turn is based on one by [31] and which uses the baby steps/giant steps algorithm design technique, can be adapted to the dense integer matrix determinant problem and then has bit complexity. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

2002 article

Efficient matrix preconditioners for black box linear algebra

Chen, L., Eberly, W., Kaltofen, E., Saunders, B. D., Turner, W. J., & Villard, G. (2002, March 1). Linear Algebra and Its Applications, Vol. 343, pp. 119–146.

By: L. Chen *, W. Eberly*, E. Kaltofen n , B. Saunders*, W. Turner n & G. Villard *

Contributors: L. Chen *, W. Eberly*, E. Kaltofen n , B. Saunders*, W. Turner n & G. Villard *

author keywords: black box matrix; sparse matrix; structured matrix; Toeplitz-like matrix; matrix preconditioner; exact arithmetic; finite field; symbolic computation; linear system solution; minimal polynomial; characteristic polynomial; rank; determinant; Wiedemann algorithm; randomized algorithm; butterfly network
topics (OpenAlex): Matrix Theory and Algorithms; Electromagnetic Scattering and Analysis; Coding theory and cryptography
TL;DR: Improvements are offered for the efficiency and applicability of preconditioners on linear algebra problems over finite fields, but most results are valid for entries from arbitrary fields. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2002 conference paper

LINBOX: A GENERIC LIBRARY FOR EXACT LINEAR ALGEBRA

Mathematical Software. Presented at the Proceedings of the First International Congress of Mathematical Software.

By: J. Dumas *, T. Gautier*, M. Giesbrecht*, P. Giorgi *, B. Hovinen*, E. Kaltofen* , B. Saunders*, W. Turner*, G. Villard *

topics (OpenAlex): Matrix Theory and Algorithms; Polynomial and algebraic computation; Mathematics and Applications
TL;DR: The design of this generic library LinBox is described, its current range of capabilities are sketched, its guiding design principle of re-usability is given, and several examples of its use are given. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

2001 conference paper

Algorithms for sparse and black box matrices over finite fields

Kaltofen, E. (2001, May 23). Presented at the International Conference on Finite Fields and Applications, Oaxaca, Mexico.

By: E. Kaltofen 

Event: International Conference on Finite Fields and Applications at Oaxaca, Mexico

Source: NC State University Libraries
Added: March 26, 2022

2000 article

Challenges of Symbolic Computation: My Favorite Open Problems

Kaltofen, E. (2000, June 1). Journal of Symbolic Computation, Vol. 29, pp. 891–919.

By: E. Kaltofen n 

Contributors: E. Kaltofen n 

topics (OpenAlex): Polynomial and algebraic computation; Complexity and Algorithms in Graphs; Cryptography and Data Security
TL;DR: The author presents background to each of his problems and a clear-cut test that evaluates whether a proposed attack has solved one of my problems, and state his favorite eight open problems in symbolic computation. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2000 conference paper

Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel's algorithm

Proceedings of the 2000 international symposium on Symbolic and algebraic computation symbolic and algebraic computation - ISSAC '00, 192–201.

By: E. Kaltofen n , W. Lee  n & A. Lobo*

Contributors: E. Kaltofen n , W. Lee  n & A. Lobo*

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Numerical Methods and Algorithms
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1999 article

Distributed Matrix-Free Solution of Large Sparse Linear Systems over Finite Fields

Kaltofen, E., & Lobo, A. (1999, July 1). Algorithmica, Vol. 24, pp. 331–348.

By: E. Kaltofen n  & A. Lobo*

Contributors: E. Kaltofen n  & A. Lobo*

author keywords: distributed symbolic computation; sparse linear systems; block Wiedemann; outer loop parallelization
topics (OpenAlex): Parallel Computing and Optimization Techniques; Cryptography and Residue Arithmetic; Polynomial and algebraic computation
TL;DR: An outer loop parallelization that works well in conjunction with a black box abstraction for the coefficient matrix is performed that can be run on a network cluster of UNIX workstations as well as on an SP-2 multiprocessor. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

1999 journal article

East Coast Computer Algebra Day '99 (April 24, 1999): Abstracts of invited talks and presented posters

Association for Computing Machinery SIGSAM Bulletin, 33(2), 43–52.

By: H. Hong  n, E. Kaltofen n  & M. Singer  n

Ed(s): H. Hong  n, E. Kaltofen n  & M. Singer  n

topics (OpenAlex): Complexity and Algorithms in Graphs; Advanced Graph Theory Research; Polynomial and algebraic computation
TL;DR: All photographs courtesy of Hoon Hong Erich Kaltofen, Michael Singer and Michael Singer. (via Semantic Scholar)
Sources: NC State University Libraries, NC State University Libraries
Added: March 26, 2022

1999 conference paper

Efficient algorithms for computing the nearest polynomial with a real root and related problems

Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99. Presented at the the 1999 international symposium.

By: M. Hitz*, E. Kaltofen n  & Y. Lakshman*

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Iterative Methods for Nonlinear Equations
TL;DR: Three new algorithms in the general area of input-sensitivity analysis are presented: a problem formulation, possibly with floating point coefficients, lacks an expected property because the inputs are slightly perturbed, and a task is to efficiently compute the nearest problem that has the desired property. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1999 conference paper

On the genericity of the modular polynomial GCD algorithm

Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99. Presented at the the 1999 international symposium.

By: E. Kaltofen n  & M. Monagan *

topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation; Tensor decomposition and applications
TL;DR: This paper develops the algorithm for multivariate polynomials over Euclidean domains which have a special kind of remainder function and applies this generic algorithm to a GCD problem in Z/(p)[t][x] where p is small, yielding an improved asymptotic performance over the usual approach. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1999 conference paper

Symbolic computation in Java

Proceedings of the 1999 international symposium on Symbolic and algebraic computation - ISSAC '99. Presented at the the 1999 international symposium.

By: L. Bernardin*, B. Char * & E. Kaltofen n 

topics (OpenAlex): Logic, programming, and type systems; Formal Methods in Verification; Parallel Computing and Optimization Techniques
TL;DR: This article discusses Java as a symbolic computation development tool, expanding on the pioneering efforts of other researchers and investigates if Java can compete with C++, or Maple/Mathematica/Axiom for efficient programming. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1998 chapter

Algebraic Algorithms

In Algorithms and Theory of Computation Handbook.

By: A. Díaz, I. Emiris, E. Kaltofen*  & V. Pan

topics (OpenAlex): Polynomial and algebraic computation
TL;DR: This is a preliminary version of a Chapter on Algebraic Algorithms in the upcoming Computing Handbook Set Computer Science (Volume I), CRC Press/Taylor and Francis Group. (via Semantic Scholar)
Source: Crossref
Added: January 21, 2021

1998 conference paper

Efficient algorithms for computing the nearest polynomial with constrained roots

Proceedings of the 1998 international symposium on Symbolic and algebraic computation - ISSAC '98, 236–243.

By: M. Hitz* & E. Kaltofen n 

Contributors: M. Hitz* & E. Kaltofen n 

topics (OpenAlex): Numerical Methods and Algorithms; Polynomial and algebraic computation; Complexity and Algorithms in Graphs
TL;DR: This work gives a polynomial-time algorithm to compute the radius of stability in the Euclidean norm for a variety of stability domains and develops hybrid symbolic-numeric algorithms to constrain one root of a complex or realPolynomial to a curve in the complex plane. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1998 conference paper

FOXBOX

Proceedings of the 1998 international symposium on Symbolic and algebraic computation - ISSAC '98. Presented at the the 1998 international symposium.

By: A. Díaz* & E. Kaltofen n 

topics (OpenAlex): Cellular Automata and Applications; Algorithms and Data Compression; Logic, programming, and type systems
TL;DR: A software package that puts in practice the black box representation of symbolic objects and provides algorithms for performing the symbolic calculus with such representations is introduced and the results of several challenge problems are presented, representing the first symbolic solutions of such problems. (via Semantic Scholar)
Source: Crossref
Added: August 28, 2020

1998 conference paper

FoxBox: a system for manipulating symbolic objects in black box representation

Proceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC, 30–37. http://www.scopus.com/inward/record.url?eid=2-s2.0-0032514311&partnerID=MN8TOARS

By: A. Diaz & E. Kaltofen 

Contributors: A. Diaz & E. Kaltofen 

www.scopus.com
Source: ORCID
Added: April 22, 2025

1998 article

Subquadratic-time factoring of polynomials over finite fields

Kaltofen, E., & Shoup, V. (1998, January 1). Mathematics of Computation, Vol. 67, pp. 1179–1197.

By: E. Kaltofen n  & V. Shoup *

Contributors: E. Kaltofen n  & V. Shoup *

author keywords: factoring; polynomials; finite fields; randomized algorithms; normal bases
topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation; Cryptography and Residue Arithmetic
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

1997 chapter

Algebraic algorithms

In A. B. Tucker (Ed.), The computer science and engineering handbook (pp. 226–248). Boca Raton, Florida: CRC Press.

By: A. Díaz, E. Kaltofen  & V. Pan

Ed(s): A. Tucker

Source: NC State University Libraries
Added: March 26, 2022

1997 conference paper

Fast polynomial factorization over high algebraic extensions of finite fields

Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97, 184–188.

By: E. Kaltofen n  & V. Shoup *

Contributors: E. Kaltofen n  & V. Shoup *

topics (OpenAlex): Coding theory and cryptography; Cryptography and Residue Arithmetic; Cryptographic Implementations and Security
TL;DR: New algorithms are presented for factoring polynomials of degree n over the finite field of q elements, where q is a power of a fixed prime number, and these algorithms are asymptotically faster than previous known algorithms. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1997 conference paper

On randomized Lanczos algorithms

Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97, 176–183.

By: W. Eberly* & E. Kaltofen n 

Contributors: W. Eberly* & E. Kaltofen n 

topics (OpenAlex): Complexity and Algorithms in Graphs; Computational Geometry and Mesh Generation; Data Management and Algorithms
TL;DR: Las Vegas algorithms that are based on Lanczos’s method for solving symmetric linear systems are presented and analyzed and suggest that these Lanczos algorithms are preferable to several versions of Wiedemann's method for computations over large fields, especially for certain symmetric matrix computations. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1997 book

PASCO '97: Proceedings of the second international symposium on Parallel symbolic computation

Erich Kaltofen

Ed(s): H. Hong, E. Kaltofen  & M. Hitz

topics (OpenAlex): Graph Theory and Algorithms; Constraint Satisfaction and Optimization
Sources: Crossref, NC State University Libraries
Added: June 15, 2021

1997 article

Teaching Computational Abstract Algebra

KALTOFEN, E. R. I. C. H. (1997, May 1). Journal of Symbolic Computation, Vol. 23, pp. 503–515.

By: E. Kaltofen n 

Contributors: E. Kaltofen n 

topics (OpenAlex): Polynomial and algebraic computation; Mathematics and Applications; Mathematical and Computational Methods
TL;DR: The topics covered and the didactical use of the corresponding Mathematica packages were described, as well as conclusions for future such courses from the students' comments and their own experience. (via Semantic Scholar)
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
4. Quality Education (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

1996 conference paper

Blocked iterative sparse linear system solvers for finite fields

In C. Roucairol (Ed.), Proceedings of the Symposium of Parallel Computing Solving Large Scale Irregular Applications (Stratagem '96) (pp. 91–95). Sophia Antipolis, France: INRIA.

By: E. Kaltofen 

Ed(s): C. Roucairol

Source: NC State University Libraries
Added: March 26, 2022

1996 conference paper

Generic Gram-Schmidt orthogonalization by exact division

Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96, 275–282.

By: Ú. Erlingsson*, E. Kaltofen n  & D. Musser*

Contributors: U. Erlingsson*, E. Kaltofen n  & D. Musser*

topics (OpenAlex): Coding theory and cryptography; semigroups and automata theory; graph theory and CDMA systems
TL;DR: This paper develops and shows how to express generic algorithms in C+so that all three possibilities are available using a single source code, and takes advantage of the genericness to test and time the algorithm using different arithmetics, including three huge-integer arithmetic packages. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1996 conference paper

On rank properties of Toeplitz matrices over finite fields

Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96, 241–249.

By: E. Kaltofen n  & A. Lobo*

Contributors: E. Kaltofen n  & A. Lobo*

topics (OpenAlex): graph theory and CDMA systems; Coding theory and cryptography; Advanced Graph Theory Research
TL;DR: These statements are proven with the extended Euclidean algorithm and the theory of subresultants that a matrix has generic rank r when all its leading principal minors up to dimension r are non-zero, and r is maximal. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1996 chapter

Prediction Based Task Scheduling in Distributed Computing

In Languages, Compilers and Run-Time Systems for Scalable Computers (pp. 317–320).

By: M. Samadani* & E. Kaltofen* 

topics (OpenAlex): Distributed and Parallel Computing Systems; Cloud Computing and Resource Management; Parallel Computing and Optimization Techniques
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1995 journal article

Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems

Mathematics of Computation, 64(210), 777–777.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Matrix Theory and Algorithms; Coding theory and cryptography
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1995 journal article

Effective Noether Irreducibility Forms and Applications

Journal of Computer and System Sciences, 50(2), 274–295.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation; Cryptography and Residue Arithmetic
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1995 journal article

Integer division in residue number systems

IEEE Transactions on Computers, 44(8), 983–989.

By: M. Hitz* & E. Kaltofen* 

Contributors: M. Hitz* & E. Kaltofen* 

author keywords: INTEGER DIVISION; RECIPROCAL; NEWTON ITERATION; EXTENDED RESIDUE NUMBER SYSTEM; MIXED RADIX CONVERSION; BASE EXTENSION
topics (OpenAlex): Cryptography and Residue Arithmetic; Coding theory and cryptography; Numerical Methods and Algorithms
TL;DR: This contribution to the ongoing discussion of division algorithm for residue number systems (RNS) is based on Newton iteration for computing the reciprocal, and an extended RNS with twice the number of moduli provides the range required for multiplication and scaling. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1995 conference paper

On computing greatest common divisors with polynomials given by black boxes for their evaluations

In A. H. M. Levelt (Ed.), Proceedings of the 1995 international symposium on Symbolic and algebraic computation - ISSAC '95 (pp. 232–239).

By: A. Díaz* & E. Kaltofen* 

Contributors: A. Diaz* & E. Kaltofen* 

Ed(s): A. Levelt

topics (OpenAlex): Polynomial and algebraic computation; Commutative Algebra and Its Applications; Complexity and Algorithms in Graphs
TL;DR: This work revisits the problem of computing the greatest common divisor (GCD) in black box format of several multivariate polynomials that themselves are given by black boxes and presents an improved version of the algorithm sketched in Kaltofen and Trager. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

1995 journal article

Process Scheduling in DSC and the Large Sparse Linear Systems Challenge

Journal of Symbolic Computation, 19(1-3), 269–282.

By: A. Dı́az *, M. Hitz*, E. Kaltofen* , A. Lobo* & T. Valente *

Contributors: A. Díaz *, M. Hitz*, E. Kaltofen* , A. Lobo* & T. Valente *

topics (OpenAlex): Parallel Computing and Optimization Techniques; Distributed and Parallel Computing Systems; Low-power high-performance VLSI design
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1994 chapter

A Distributed Approach to Problem Solving in Maple

In Maple V: Mathematics and its Applications (pp. 13–21).

By: K. Chan*, A. Díaz * & E. Kaltofen* 

topics (OpenAlex): Advanced Database Systems and Queries; Polynomial and algebraic computation; Data Management and Algorithms
TL;DR: A system is described whereby a Maple computation can be distributed across a network of computers running Unix, based on the DSC system, which can ship source code and input data to carefully selected computers for execution and which can retrieve the produced output data. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1994 conference paper

Asymptotically fast solution of Toeplitz-like singular linear systems

Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94, Part F129423, 297–304.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Complexity and Algorithms in Graphs; Advanced Graph Theory Research
TL;DR: The problem of computing a solution to a possibly singular linear system Ax = b with coefficients in an arbitrary field, where A is an N ×N matrix of displacement rank α given in ΣLU representation is considered and it is shown that if the system is solvable the authors can find a vector that is uniformly sampled from the solution manifold in O(αN( log N) loglog N) expected arithmetic operations in the field of entries. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1994 conference paper

Factoring high-degree polynomials by the black box Berlekamp algorithm

Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94, Part F129423, 90–98.

By: E. Kaltofen*  & A. Lobo*

Contributors: E. Kaltofen*  & A. Lobo*

topics (OpenAlex): Polynomial and algebraic computation; Advanced Combinatorial Mathematics; graph theory and CDMA systems
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1994 conference paper

Parallel solution of Toeplitz and Toeplitz-like linear systems over fields of small positive characteristic

In H. Hong (Ed.), Proceedings of the First International Symposium of Parallel Symbolic Computation (pp. 225–233). Singapore: World Scientific Publishing Co.

By: E. Kaltofen  & V. Pan

Ed(s): H. Hong

Source: NC State University Libraries
Added: March 26, 2022

1993 chapter

Analysis of Coppersmith's block Wiedemann algorithm for the parallel solution of sparse linear systems

In Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: Vol. 673 LNCS (pp. 195–212).

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Coding theory and cryptography; Matrix Theory and Algorithms; Complexity and Algorithms in Graphs
TL;DR: It is proved that by use of certain randomizations on the input system the parallel speed up is roughly by the number of vectors in the blocks when using as many processors. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1993 report

Computational differentiation and algebraic complexity theory

In C. H. Bischof, A. Griewank, & P. M. Khademi (Eds.), Workshop Report on First Theory Institute on Computational Differentiation (Technical Report No. ANL/MCS-TM-183; pp. 28–30). Argonne, Illinois: Argonne National Laboratory.

By: E. Kaltofen 

Ed(s): C. Bischof, A. Griewank & P. Khademi

Source: NC State University Libraries
Added: March 26, 2022

1993 journal article

Direct proof of a theorem by Kalkbrener, Sweedler, and Taylor

ACM SIGSAM Bulletin, 27(4), 2.

By: E. Kaltofen* 

topics (OpenAlex): Coding theory and cryptography; graph theory and CDMA systems; Analytic Number Theory Research
TL;DR: This note presents a direct proof of the following fact: Kalkbrener, Sweedler, and Taylor (1993) present degree bounds on the coefficients needed to express 1 (and other low degree polynomials) asigma. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1993 chapter

Dynamic parallel evaluation of computation DAGs

In J. Reif (Ed.), Synthesis of Parallel Algorithms (pp. 723–758). San Mateo, California: Morgan Kaufmann Publishers.

By: E. Kaltofen 

Ed(s): J. Reif

Source: NC State University Libraries
Added: March 26, 2022

1992 report

Efficient solution of sparse linear systems

[Lecture Notes]. Troy, New York: Rensselaer Polytechnic Institute, Department of Computer Science.

By: E. Kaltofen 

Source: NC State University Libraries
Added: March 26, 2022

1992 conference paper

On computing determinants of matrices without divisions

Papers from the international symposium on Symbolic and algebraic computation - ISSAC '92, Part F129620, 342–349.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): graph theory and CDMA systems; Polynomial and algebraic computation; Advanced Graph Theory Research
TL;DR: An algorithm that computes the determinant of an n x n matrix with entries fr~rn an arbitrary commutative ring in 0(n3~ ring additions, subtractions, and multiplications; the ‘soft-O’ O indicates some missing log n factors. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1992 book

Preface

In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. V-VI). http://www.scopus.com/inward/record.url?eid=2-s2.0-85029801885&partnerID=MN8TOARS

By: E. Kaltofen  & R. Zippel

Contributors: E. Kaltofen  & R. Zippel

www.scopus.com
Source: ORCID
Added: April 22, 2025

1992 conference paper

Processor-efficient parallel solution of linear systems. II. The positive characteristic and singular cases

Proceedings., 33rd Annual Symposium on Foundations of Computer Science, 1992-October, 714–723.

By: E. Kaltofen*  & V. Pan *

Contributors: E. Kaltofen*  & V. Pan *

topics (OpenAlex): Complexity and Algorithms in Graphs; Matrix Theory and Algorithms; Parallel Computing and Optimization Techniques
TL;DR: The authors show that over any field, the solution set to a system of n linear equations in n unknowns can be computed in parallel with randomization simultaneously in poly-logarithmic time in n and with only as many processors as are utilized to multiply two n * n matrices. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1991 conference paper

DSC: a system for distributed symbolic computation

In S. M. Watt (Ed.), Proceedings of the 1991 international symposium on Symbolic and algebraic computation - ISSAC '91 (pp. 323–332).

By: A. Diaz *, E. Kaltofen* , K. Schmitz *, M. Hitz, A. Lobo, T. Valente *, P. Smyth

Contributors: A. Diaz *, E. Kaltofen* , K. Schmitz *, M. Hitz, A. Lobo, T. Valente *, P. Smyth

Ed(s): S. Watt

topics (OpenAlex): Algorithms and Data Compression; Cellular Automata and Applications; DNA and Biological Computing
TL;DR: This work has tested DSC with a primality test for large integers and with a factorization algorithm for polynomials over large finite fields and observed significant speed-ups over executing the best-known methods on a single workstation computation. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

1991 conference paper

Effective Noether irreducibility forms and applications

Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91. Presented at the the twenty-third annual ACM symposium.

By: E. Kaltofen* 

topics (OpenAlex): Cryptography and Data Security; Computational Geometry and Mesh Generation; Parallel Computing and Optimization Techniques
TL;DR: The “single path lazy factorization” representation model for elements in algebraic extension fields is introduced, with which the problem of factoring polynomials with rational number or rational function coefficients can be solved within the parallel computational complexity class MC. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1991 conference paper

Effective noether irreducibility forms and applications (Extended Abstract)

Proceedings of the Annual ACM Symposium on Theory of Computing, Part F130073, 54–63. http://www.scopus.com/inward/record.url?eid=2-s2.0-85031923272&partnerID=MN8TOARS

By: E. Kaltofen 

Contributors: E. Kaltofen 

www.scopus.com
Source: ORCID
Added: April 22, 2025

1991 chapter

Explicit Construction of the Hilbert Class Fields of Imaginary Quadratic Fields by Integer Lattice Reduction

In D. V. Chudnovsky, G. V. Chudnovsky, H. Cohn, & M. B. Nathanson (Eds.), Number Theory (pp. 149–202).

By: E. Kaltofen*  & N. Yui*

Ed(s): D. Chudnovsky, G. Chudnovsky, H. Cohn & M. Nathanson

topics (OpenAlex): Algebraic Geometry and Number Theory; Analytic Number Theory Research; Polynomial and algebraic computation
Sources: Crossref, NC State University Libraries
Added: June 15, 2021

1991 journal article

On fast multiplication of polynomials over arbitrary algebras

Acta Informatica, 28(7), 693–701.

By: D. Cantor* & E. Kaltofen* 

Contributors: D. Cantor & E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Commutative Algebra and Its Applications
TL;DR: This paper generalizes the well-known Sch6nhage-Strassen algorithm for multiplying large integers to an algorithm for dividing polynomials with coefficients from an arbitrary, not necessarily commutative, not always associative, algebra d, and obtains a method not requiring division that is valid for any algebra. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1991 chapter

On wiedemann's method of solving sparse linear systems

In H. F. Mattson, T. Mora, & T. R. N. Rao (Eds.), Applied Algebra, Algebraic Algorithms and Error-Correcting Codes: Vol. 539 LNCS (pp. 29–38).

By: E. Kaltofen*  & B. Saunders*

Contributors: E. Kaltofen*  & B. Saunders*

Ed(s): H. Mattson, T. Mora & T. Rao

topics (OpenAlex): Matrix Theory and Algorithms; Polynomial and algebraic computation; Computational Geometry and Mesh Generation
TL;DR: Douglas Wiedemann’s (1986) landmark approach to solving sparse linear systems over finite fields provides the symbolic counterpart to non-combinatorial numerical methods for solving sparselinear systems, such as the Lanczos or conjugate gradient method. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

1991 conference paper

Processor efficient parallel solution of linear systems over an abstract field

Proceedings of the third annual ACM symposium on Parallel algorithms and architectures - SPAA '91, 180–191.

By: E. Kaltofen*  & V. Pan *

Contributors: E. Kaltofen*  & V. Pan *

topics (OpenAlex): Complexity and Algorithms in Graphs; Parallel Computing and Optimization Techniques; Optimization and Search Problems
TL;DR: Parallel randomized algorithms are presented that solve n-dimensional systems of linear equations and compute inverses of n × n non-singular matrices over a field in O((log n)) time, where each time unit represents an arithmetic operation in the field generated by the matrix entries. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1991 conference paper

Size efficient parallel algebraic circuits for partial derivatives

In D. V. Shirkov, V. A. Rostovtsev, & V. P. Gerdt (Eds.), IV International Conference on Computer Algebra in Physical Research (pp. 133–145). Singapore: World Scientific Publishing Co.

By: E. Kaltofen  & M. Singer

Ed(s): D. Shirkov, V. Rostovtsev & V. Gerdt

Source: NC State University Libraries
Added: March 26, 2022

1990 journal article

Algebraic Computational Complexity

Journal of Symbolic Computation, 9(3).

Erich Kaltofen

Ed(s): E. Kaltofen 

Source: NC State University Libraries
Added: March 26, 2022

1990 conference paper

Computer mathematics systems and a trilateral approach to human resource development in technical occupations

In N. Estes, J. Heene, & D. Leclercq (Eds.), Proceedings of the 7th International Conference on Technology and Education (Vol. 1, pp. 251–253). Edinburgh, United Kingdom: CEP Consultants Ltd.

By: D. Rebne & E. Kaltofen 

Ed(s): N. Estes, J. Heene & D. Leclercq

Source: NC State University Libraries
Added: March 26, 2022

1990 journal article

Computing the irreducible real factors and components of an algebraic curve

Applicable Algebra in Engineering, Communication and Computing, 1(2), 135–148.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Cryptography and Data Security; Computational Geometry and Mesh Generation
TL;DR: These algorithms are of polynomial bit complexity in the degree of the equation and the size of its coefficients and are based on computing the irreducible complex factors and then investigating high precision complex floating point coefficients of these factors and the complex norms. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1990 journal article

Computing with polynomials given byblack boxes for their evaluations: Greatest common divisors, factorization, separation of numerators and denominators

Journal of Symbolic Computation, 9(3), 301–320.

By: E. Kaltofen*  & B. Trager*

Contributors: E. Kaltofen*  & B. Trager*

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Cryptography and Residue Arithmetic
Sources: Crossref, ORCID, NC State University Libraries
Added: January 24, 2021

1990 conference paper

Modular rational sparse multivariate polynomial interpolation

Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '90, 135–139.

By: E. Kaltofen* , Y. Lakshman* & J. Wiley*

Contributors: E. Kaltofen* , Y. Lakshman* & J. Wiley*

topics (OpenAlex): Advanced Numerical Analysis Techniques; Polynomial and algebraic computation; Digital Filter Design and Implementation
TL;DR: The computing times for the speeded Ben-Or and Tiwari and the modular algorithm are compared, and it is shown that the modular algorithms is markedly superior. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1990 journal article

Parallel algorithms for matrix normal forms

Linear Algebra and Its Applications, 136(C), 189–208.

By: E. Kaltofen* , M. Krishnamoorthy* & B. Saunders*

Contributors: E. Kaltofen* , M. Krishnamoorthy* & B. Saunders*

topics (OpenAlex): Complexity and Algorithms in Graphs; Cryptography and Data Security; Polynomial and algebraic computation
TL;DR: A new randomized parallel algorithm that determines the Smith normal form of a matrix with entries being univariate polynomials with coefficients in an arbitrary field that is probabilistic of Las Vegas type and reduces the problem of Smith form computation to two Hermite form computations. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

1990 chapter

Polynomial factorization 1982-1986

In D. V. Chudnovsky & R. D. Jenks (Eds.), Computers in Mathematics, Lecture Notes in Pure and Applied Mathematics (Vol. 125, pp. 285–309). New York, NY: Marcel Dekker, Inc.

By: E. Kaltofen 

Ed(s): D. Chudnovsky & R. Jenks

Source: NC State University Libraries
Added: March 26, 2022

1990 article

Special issue computational algebraic complexity editorial

Kaltofen, E., & Buchberger, B. (1990, March 1). Journal of Symbolic Computation, Vol. 9, pp. 225–228.

By: E. Kaltofen*  & B. Buchberger

Contributors: E. Kaltofen*  & B. Buchberger

topics (OpenAlex): Advanced Algebra and Logic; Computability, Logic, AI Algorithms; Polynomial and algebraic computation
Source: ORCID
Added: April 22, 2025

1989 conference paper

An improved Las Vegas primality test

Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89, Part F130182, 26–33.

By: E. Kaltofen* , T. Valente * & N. Yui*

Contributors: E. Kaltofen* , T. Valente * & N. Yui*

topics (OpenAlex): Algebraic Geometry and Number Theory; Cryptography and Residue Arithmetic; Polynomial and algebraic computation
TL;DR: A modification of the Goldwasser-Kilian-Atkin primality test, which, when given an input n, outputs either prime or composite, along with a certificate of correctness which may be verified in polynomial time. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1989 book

Computers and Mathematics

(E. Kaltofen & S. M. Watt, Eds.).

By: E. Kaltofen*  & S. Watt

Ed(s): E. Kaltofen*  & S. Watt

topics (OpenAlex): Computability, Logic, AI Algorithms
TL;DR: This volume contains the contributed papers accepted for presentation, selected from 85 drafts submitted in response to the call for papers. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: June 15, 2021

1989 journal article

Computing greatest common divisors and factorizations in quadratic number fields

Mathematics of Computation, 53(188), 697–697.

By: E. Kaltofen*  & H. Rolletschek*

Contributors: E. Kaltofen*  & H. Rolletschek*

topics (OpenAlex): Coding theory and cryptography; Algebraic Geometry and Number Theory; Analytic Number Theory Research
TL;DR: It is shown that there does not even exist an input in these domains for which the GCD computation becomes possible by allowing nondecreasing norms or remainders whose norms are not as small as possible. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1989 conference paper

Computing the irreducible real factors and components of an algebraicf curve

In K. Mehlhorn (Ed.), Proceedings of the fifth annual symposium on Computational geometry - SCG '89: Vol. Part F130124 (pp. 79–87).

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

Ed(s): K. Mehlhorn

topics (OpenAlex): Polynomial and algebraic computation; Cryptography and Residue Arithmetic; Coding theory and cryptography
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

1989 chapter

Factorization of polynomials given by straight-line programs

In S. Micali (Ed.), Randomness and Computation, Advances in Computing Research (Vol. 5, pp. 375–412). Greenwhich, Connecticut: JAI Press Inc.

By: E. Kaltofen 

Ed(s): S. Micali

Source: NC State University Libraries
Added: March 26, 2022

1989 chapter

Improved sparse multivariate polynomial interpolation algorithms

In Symbolic and Algebraic Computation: Vol. 358 LNCS (pp. 467–474).

By: E. Kaltofen*  & L. Yagati*

Contributors: E. Kaltofen*  & L. Yagati*

topics (OpenAlex): Polynomial and algebraic computation; Tensor decomposition and applications; Advanced Numerical Analysis Techniques
TL;DR: This work considers the problem of interpolating sparse multivariate polynomials from their values and presents efficient algorithms for finding the rank of certain special Toeplitz systems arising in the Ben-Or and Tiwari algorithm and for solving transposed Vandermonde systems of equations. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

1989 chapter

Mr. Smith goes to Las Vegas: Randomized parallel computation of the Smith Normal form of polynomial matrices

In Lecture Notes in Computer Science: Vol. 378 LNCS (pp. 317–322).

By: E. Kaltofen* , M. Krishnamoorthy* & B. Saunders*

Contributors: E. Kaltofen* , M. Krishnamoorthy* & B. Saunders*

topics (OpenAlex): Polynomial and algebraic computation; Complexity and Algorithms in Graphs; Matrix Theory and Algorithms
TL;DR: The method employs randomization as a tool to remove the iterations along the main diagonal in the classical sequential algorithms, and as such might be useful in similar settings, as well as may speed the sequential methods themselves. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1989 conference paper

Parallel algebraic algorithm design

Kaltofen, E. (1989, July). Presented at the 1989 International Symposium on Symbolic and Algebraic Computation, Portland, Oregon.

By: E. Kaltofen 

Event: 1989 International Symposium on Symbolic and Algebraic Computation at Portland, Oregon

Source: NC State University Libraries
Added: March 26, 2022

1989 conference paper

Solving systems of nonlinear polynomial equations faster

Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89, Part F130182, 121–128.

By: J. Canny *, E. Kaltofen*  & L. Yagati*

Contributors: J. Canny *, E. Kaltofen*  & L. Yagati*

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Complexity and Algorithms in Graphs
TL;DR: This paper considers projective problems, that is, the polynomials are homogeneous and the solutions are sought in n-dimensional projective space, and shows that the solutions of an affine system are specializations of the solution rays of its homogenized projective version. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: January 24, 2021

1988 journal article

Analysis of the binary complexity of asymptotically fast algorithms for linear system solving

ACM SIGSAM Bulletin, 22(2), 41–49.

By: B. Gregory * & E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Advanced Combinatorial Mathematics
TL;DR: Two significant developments can be distinguished in the theory of algebraic algorithm design: that of fast algorithms in terms of counting the arithmetic operations, and the actual bit complexity when such algorithms are performed for concrete fields, in particular the rational numbers. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1988 conference paper

Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators

[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science, 296–305.

By: E. Kaltofen*  & B. Trager*

Contributors: E. Kaltofen*  & B. Trager*

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Numerical Methods and Algorithms
TL;DR: Algorithms are developed that adopt a novel implicit representation for multivariate polynomials and rational functions with rational coefficients, that of black boxes for their evaluation, and it is shown that within this evaluation-box representation, the polynomial greatest common divisor and factorization problems as well as the problem of extracting the numerator and denominator of a rational function can be solved in random polynometric time. (via Semantic Scholar)
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4. Quality Education (OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1988 journal article

Dagwood: a system for manipulating polynomials given by straight-line programs

ACM Transactions on Mathematical Software, 14(3), 218–240.

By: T. Freeman*, G. Imirzian*, E. Kaltofen*  & L. Yagati*

Contributors: T. Freeman*, G. Imirzian*, E. Kaltofen*  & L. Yagati*

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Logic, programming, and type systems
TL;DR: This work discusses the design, implementation, and benchmarking of a system that can manipulate symbolic expressions represented by their straight-line computations capable of performing rational arithmetic on, evaluating, differentiating, taking greatest common divisors of, and factoring polynomials instraight-line format. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1988 journal article

Efficient Parallel Evaluation of Straight-Line Code and Arithmetic Circuits

SIAM Journal on Computing, 17(4), 687–695.

By: G. Miller *, V. Ramachandran* & E. Kaltofen* 

Contributors: G. Miller *, V. Ramachandran* & E. Kaltofen* 

topics (OpenAlex): Coding theory and cryptography; Low-power high-performance VLSI design; Numerical Methods and Algorithms
TL;DR: A new parallel algorithm is given to evaluate a straight line program over a commutative semi-ring R of degree d and size n in time O(log n( log nd)) using M(n) processors, where M( n) is the number of processors required for multiplying n×n matrices over the semi- ring R in O (log n) time. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1988 journal article

Greatest common divisors of polynomials given by straight-line programs

Journal of the ACM, 35(1), 231–264.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Numerical Methods and Algorithms; Commutative Algebra and Its Applications
TL;DR: It is shown that most algebraic algorithms can be probabilistically applied to data that are given by a straight-line computation, and every degree-bounded rational function can be computed fast in parallel, that is, in polynomial size and polylogarithmic depth. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1987 journal article

Computer Algebra Algorithms

Annual Review of Computer Science, 2(1), 91–118.

By: E. Kaltofen* 

topics (OpenAlex): Commutative Algebra and Its Applications; Polynomial and algebraic computation; Algebraic structures and combinatorial models
TL;DR: A systematic review of Integer and Polynomial Addition, Multiplication, and Division with Remainder and its applications in Language and System Design and Decision Methods for Elementary Algebr a and Geometry. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1987 journal article

Deterministic irreducibility testing of polynomials over large finite fields

Journal of Symbolic Computation, 4(1), 77–82.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Algorithms and Data Compression; Coding theory and cryptography; Cryptographic Implementations and Security
TL;DR: This work presents a sequential deterministic polynomial-time algorithm for testing dense multivariate polynomials over a large finite field for irreducibility, based on the algorithm for absolute irreduceibility testing combined with Berlekamp's algorithm. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1987 journal article

Fast Parallel Computation of Hermite and Smith Forms of Polynomial Matrices

SIAM Journal on Algebraic Discrete Methods, 8(4), 683–690.

By: E. Kaltofen* , M. Krishnamoorthy & B. Saunders

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Complexity and Algorithms in Graphs
TL;DR: A polynomial-time deterministic sequential algorithm for the Smith normal form over the rationals, which is applied to the rational canonical form of matrices over finite fields and the field of rational numbers. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1987 report

Fast multiplication of polynomials over arbitrary rings

(Technical Report No. 87-35). Troy, NY: Rensselaer Polytechnic Institute, Department of Computer Science.

By: D. Cantor & E. Kaltofen 

Source: NC State University Libraries
Added: March 26, 2022

1987 conference paper

Single-factor Hensel lifting and its application to the straight-line complexity of certain polynomials

Proceedings of the nineteenth annual ACM conference on Theory of computing - STOC '87, 443–452.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): semigroups and automata theory; Complexity and Algorithms in Graphs; Commutative Algebra and Its Applications
TL;DR: Three theorems are presented that establish polynomial straight-line complexity for certain operations on polynomials given bystraight-line programs of unbounded input degree, and a higher order partial derivative in a single variable is shown. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1986 conference paper

A system for manipulating polynomials given by straight-line programs

Proceedings of the fifth ACM symposium on Symbolic and algebraic computation - SYMSAC '86. Presented at the the fifth ACM symposium.

By: T. Freeman*, G. Imirzian* & E. Kaltofen* 

topics (OpenAlex): Complexity and Algorithms in Graphs; Numerical Methods and Algorithms; Parallel Computing and Optimization Techniques
TL;DR: This work discusses the design, implementation, and benchmarking of a system that can manipulate symbolic expressions represented by their straight-line computations capable of performing rational arithmetic, evaluating, differentiating, taking greatest common divisors of, and factoring polynomials instraight-line format. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1986 chapter

Efficient parallel evaluation of straight-line code and arithmetic circuits

In VLSI Algorithms and Architectures: Vol. 227 LNCS (pp. 236–245).

By: G. Miller *, V. Ramachandran* & E. Kaltofen* 

Contributors: G. Miller *, V. Ramachandran* & E. Kaltofen* 

topics (OpenAlex): Numerical Methods and Algorithms; Parallel Computing and Optimization Techniques; VLSI and Analog Circuit Testing
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1986 conference paper

Fast parallel algorithms for similarity of matrices

Proceedings of the fifth ACM symposium on Symbolic and algebraic computation - SYMSAC '86. Presented at the the fifth ACM symposium.

By: E. Kaltofen* , M. Krishnamoorthy* & B. Saunders*

topics (OpenAlex): Complexity and Algorithms in Graphs; Advanced Graph Theory Research; Optimization and Search Problems
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1986 conference paper

Uniform closure properties of P-computable functions

Proceedings of the eighteenth annual ACM symposium on Theory of computing - STOC '86. Presented at the the eighteenth annual ACM symposium.

By: E. Kaltofen* 

topics (OpenAlex): Cryptography and Data Security; Complexity and Algorithms in Graphs; Computability, Logic, AI Algorithms
TL;DR: The question of whether pcomputable families would be closed under natural mathematics operations was raised and it was shown that by taking repeated part ial derivatives in a single variable one can obtain the general permanent from a polynomial-sized formula. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1985 article

Arithmetic in quadratic fields with unique factorization

Kaltofen, E., & Rolletschek, H. (1985, January 1). Lecture Notes in Computer Science, pp. 279–288.

By: E. Kaltofen*  & H. Rolletschek*

Contributors: E. Kaltofen*  & H. Rolletschek*

topics (OpenAlex): Algebraic Geometry and Number Theory; Coding theory and cryptography; Polynomial and algebraic computation
Source: ORCID
Added: April 22, 2025

1985 conference paper

Computing with polynomials given by straight-line programs I: greatest common divisors

Proceedings of the seventeenth annual ACM symposium on Theory of computing - STOC '85, 131–142.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Cryptography and Residue Arithmetic
TL;DR: This work develops algorithms on multivariate polynomials represented by straight-line programs for the greatest common divisor problem and conversion to sparse representation and in random polynomial-time for the usual coefficient fields and output. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1985 conference paper

Computing with polynomials given by straight-line programs II sparse factorization

26th Annual Symposium on Foundations of Computer Science (sfcs 1985), 451–458.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Cryptography and Data Security; Complexity and Algorithms in Graphs
TL;DR: An algorithm for the factorization of a multivariate polynomial represented by a straight-line program into its irreducible factors represented as sparse polynomials is developed with controllably high probability the correct factorization. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1985 journal article

Effective Hilbert irreducibility

Information and Control, 66(3), 123–137.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Cryptography and Data Security; Cryptography and Residue Arithmetic; Coding theory and cryptography
TL;DR: A probabilistic irreducibility test for sparse multivariate poly omials over arbitrary perfect fields is constructed using a very effective version of the Hilbert Irreducible-n Theorem. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1985 journal article

Factoring sparse multivariate polynomials

Journal of Computer and System Sciences, 31(2), 265–287.

By: J. von zur Gathen* & E. Kaltofen* 

Contributors: J. Gathen* & E. Kaltofen* 

topics (OpenAlex): Cryptography and Data Security; Complexity and Algorithms in Graphs; Cryptography and Residue Arithmetic
TL;DR: A probabilistic reduction for factoring polynomials from multivariate to the bivariate case, over an arbitrary (effectively computable) field, based on an effective version of Hilbert's irreducibility theorem is presented. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1985 journal article

Factorization of multivariate polynomials over finite fields

Mathematics of Computation, 45(171), 251–251.

By: J. von zur Gathen* & E. Kaltofen* 

Contributors: J. Von Zur Gathen* & E. Kaltofen* 

topics (OpenAlex): Coding theory and cryptography; Cryptography and Data Security; Cryptography and Residue Arithmetic
TL;DR: A probabilistic algorithm that finds the irreducible factors of a bivariate polynomial with coefficients from a finite field in timePolynomial in the input size, i.e., in the degree of the polynomials and log (cardinality of field). (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

1985 journal article

Fast parallel absolute irreducibility testing

Journal of Symbolic Computation, 1(1), 57–67.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Coding theory and cryptography; Cryptographic Implementations and Security; Cryptography and Residue Arithmetic
TL;DR: It is established that the set of absolutely irreducible integral polynomials belongs to the complexity class NC of Boolean circuits of polynomial size and logarithmic depth and also to the class of sequentiallyPolynomial-time problems. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1985 journal article

Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization

SIAM Journal on Computing, 14(2), 469–489.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Coding theory and cryptography; Cryptography and Residue Arithmetic; Polynomial and algebraic computation
TL;DR: An algorithm is presented which reduces the problem of finding the irreducible factors of f in polynomial-time in the total degree of f and the coefficient lengths of f to factoring a univariate integral polynomials, which implies the following theorem. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1985 chapter

Sparse hensel lifting

In EUROCAL '85: Vol. 204 LNCS (pp. 4–17).

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Advanced Numerical Analysis Techniques; Mathematical Dynamics and Fractals
TL;DR: It is shown how the content of the input polynomial in the main variable as a by-product can be taken advantage of when computing the GCD of multivariate polynomials by sparse Hensel lifting. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1985 report

The integer manipulation techniques can compete with the linear algebra methods for solving sparse linear systems

(Technical Report No. 85-6). State University of New York at Albany, Computer Science Department.

By: E. Kaltofen  & V. Pan

Source: NC State University Libraries
Added: March 26, 2022

1984 chapter

On a theorem by R. Dedekind

In H. W. Lenstra Jr., J. K. Lenstra, & P. van Emde Boas (Eds.), DOPO LE PAROLE, Album in Honor of A. K. Lenstra's Doctorate. Amsterdam.

By: E. Kaltofen 

Ed(s): H. Lenstra, J. Lenstra & P. van Emde Boas

Source: NC State University Libraries
Added: March 26, 2022

1984 report

The algebraic theory of integration

[Lecture Notes]. Troy, New York: Rensselaer Polytechnic Institute, Department of Computer Science.

By: E. Kaltofen 

Source: NC State University Libraries
Added: March 26, 2022

1984 conference paper

The modular equation of order 11

Third Macsyma Users' Conference, 472–485. General Electric.

By: E. Kaltofen  & N. Yui

Source: NC State University Libraries
Added: March 26, 2022

1983 journal article

A Generalized Class of Polynomials that are Hard to Factor

SIAM Journal on Computing, 12(3), 473–483.

By: E. Kaltofen* , D. Musser & B. Saunders

topics (OpenAlex): Polynomial and algebraic computation
Sources: Crossref, NC State University Libraries
Added: August 28, 2020

1983 chapter

On the complexity of finding short vectors in integer lattices

In Lecture Notes in Computer Science: Vol. 162 LNCS (pp. 236–244).

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Coding theory and cryptography; graph theory and CDMA systems; Digital Image Processing Techniques
TL;DR: It is proved that this algorithm can actually be executed in O(n6(log B)2+n5( log B)3) binary steps by analyzing a modified version of the algorithm which also performs better in practice. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1983 chapter

Polynomial-time factorization of multivariate polynomials over finite fields

In Lecture Notes in Computer Science: Vol. 154. Automata, Languages and Programming (pp. 250–263).

By: J. von zur Gathen* & E. Kaltofen* 

Contributors: J. Gathen* & E. Kaltofen* 

topics (OpenAlex): Coding theory and cryptography; Cryptography and Residue Arithmetic; Cryptography and Data Security
TL;DR: A probabilistic algorithm that finds the irreducible factors of a bivariate polynomial with coefficients from a finite field in timePolynomial in the input size, i.e. in the degree of the polynomials and log (cardinality of field). (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: June 15, 2021

1982 conference paper

A polynomial reduction from multivariate to bivariate integral polynomial factorization.

Proceedings of the fourteenth annual ACM symposium on Theory of computing - STOC '82, 261–266.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Coding theory and cryptography; Algorithms and Data Compression; semigroups and automata theory
TL;DR: It is shown that testing r-variate polynomials with integer coefficients for irreducibility is m-reducible in polynomial time of the total degree and the largest coefficient length to testing bivariate polynmials for irReducibility. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1982 conference paper

A polynomial-time reduction from bivariate to univariate integral polynomial factorization

23rd Annual Symposium on Foundations of Computer Science (sfcs 1982), 57–64.

By: E. Kaltofen* 

Contributors: E. Kaltofen* 

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Cryptography and Residue Arithmetic
Sources: Crossref, ORCID
Added: August 28, 2020

1982 chapter

Factorization of Polynomials

In B. Buchberger, G. E. Collins, & R. Loos (Eds.), Computing Supplementum (pp. 95–113).

By: E. Kaltofen* 

Ed(s): B. Buchberger, G. Collins & R. Loos

topics (OpenAlex): Polynomial and algebraic computation; Coding theory and cryptography; Numerical Methods and Algorithms
Sources: Crossref, NC State University Libraries
Added: June 15, 2021

1982 thesis

On the complexity of factoring polynomials with integer coefficients

(PhD thesis). Rensselaer Polytechnic Institute, Troy, NY.

By: E. Kaltofen 

Source: NC State University Libraries
Added: March 26, 2022

1981 conference paper

A generalized class of polynomials that are hard to factor

Proceedings of the fourth ACM symposium on Symbolic and algebraic computation - SYMSAC '81, 188–194.

By: E. Kaltofen* , D. Musser & B. Saunders

Contributors: E. Kaltofen* , D. Musser & B. Saunders

topics (OpenAlex): Advanced Differential Equations and Dynamical Systems; Lipid metabolism and biosynthesis; Polynomial and algebraic computation
TL;DR: A class of univariate polynomials is defined which make the Berlekamp-Hensel factorization algorithm take an exponential amount of time. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: August 28, 2020

1981 report

An attributed LL(1) compilation of Pascal into the lambda-calculus

(Technical Report No. CS-8103). Troy, NY: Rensselaer Polytechnic Institute Mathematical Sciences Department.

By: E. Kaltofen  & S. Abdali

Source: NC State University Libraries
Added: March 26, 2022

1980 report

LISP/370 under the Michigan Terminal System

Troy, NY: Rensselaer Polytechnic Institute, Mathematical Sciences Department.

By: E. Kaltofen 

Source: NC State University Libraries
Added: March 26, 2022

Employment

Updated: August 13th, 2020 15:43

1996 - present

North Carolina State University Raleigh, NC, US
Professor Mathematics

Education

Updated: January 8th, 2021 19:27

1977 - 1981

Rensselaer Polytechnic Institute Troy, NY, US
PhD Mathematical Sciences

Funding History

Funding history based on the linked ORCID record. Updated: July 22nd, 2020 11:57

grant September 1, 2017 - August 31, 2021
AF: Small: Symbolic Computation with Certificates, Sparsity and Error Correction
Directorate for Computer & Information Science & Engineering
grant September 1, 2014 - August 31, 2018
AF: Small: Symbolic computation with sparsity, error checking and error correction
Directorate for Computer & Information Science & Engineering
grant August 1, 2011 - July 31, 2015
AF: Small: Efficient Exact/Certified Symbolic Computation By Hybrid Symbolic-Numeric and Parallel Methods
Directorate for Computer & Information Science & Engineering
grant September 1, 2008 - August 31, 2012
Model Discovery and Verification With Symbolic, Hybrid Symbolic-Numeric and Parallel Computation
Directorate for Computer & Information Science & Engineering
grant September 15, 2007 - February 28, 2010
Workshop on Advanced Cyber-Enabled Discovery & Innovation (CDI) Through Symbolic and Numeric Computation
Directorate for Computer & Information Science & Engineering
grant September 15, 2005 - August 31, 2009
Scientific Computing Research Environments for the Mathematical Sciences (SCREMS): Parallel Computer Algebra
Directorate for Mathematical & Physical Sciences
grant July 1, 2005 - June 30, 2008
Workshops for NCSU/China Research and Educational Partnership In Symbolic Computation
Office of the Director
grant June 15, 2005 - November 30, 2009
Challenges in Linear and Polynomil Algebra in Symbolic Computation Algorithms
Directorate for Computer & Information Science & Engineering
grant August 15, 2003 - December 31, 2006
Fast Bit Complexity in Symbolic Computation Algorithms
Directorate for Computer & Information Science & Engineering
grant July 15 - December 31, 2003
International Conference on Applied Computer Algebra
Directorate for Computer & Information Science & Engineering
grant July 15, 2001 - September 30, 2004
ITR/ACS: Collaborative Research LinBox: A Generic Library for Seminumeric Black Box Linear Algebra
Directorate for Computer & Information Science & Engineering
grant June 1, 2000 - August 31, 2003
Optimization, Randomization, and Generalization in Symbolic Computation
Directorate for Computer & Information Science & Engineering
grant August 15, 1999 - January 31, 2003
Scientific Computing Research Environments for the Mathematical Sciences (SCREMS)
Directorate for Mathematical & Physical Sciences
grant December 15, 1998 - November 30, 1999
East Coast Computer Algebra Day, April 24, l999, North Carolina State University, Raleigh, North Carolina
Directorate for Computer & Information Science & Engineering
grant September 15, 1997 - November 30, 2000
Multi-Use "Plug-And-Play" Software Packages for Black Box and Inexact Symbolic Objects
Directorate for Computer & Information Science & Engineering
grant July 1, 1996 - September 30, 1997
Efficient Computer Algorithms for Symbolic Mathematics
Directorate for Computer & Information Science & Engineering
grant April 15, 1994 - September 30, 1997
Efficient Computer Algorithms for Symbolic Mathematics
Directorate for Computer & Information Science & Engineering
grant February 15, 1994 - June 30, 1996
Symbolic Computation Systems for Young Scholars: Development and Industrial Applications
Directorate for Education & Human Resources
grant June 15, 1992 - May 30, 1993
Workshop for Integrated Symbolic-Number Computing; University of California, Berkeley; July, 1992
Directorate for Computer & Information Science & Engineering
grant October 15, 1991 - September 30, 1993
CISE 1991 Minority Graduate Fellowship Honorable Mention (Angel Diaz)
Directorate for Computer & Information Science & Engineering
grant March 1, 1991 - August 31, 1994
Efficient Computer Algorithms for Symbolic Mathematics
Directorate for Computer & Information Science & Engineering
grant March 15, 1990 - July 31, 1992
Symbolic Computation Systems for Young Scholars: Development and Industrial Applications
Directorate for Education & Human Resources
grant July 1, 1987 - December 31, 1990
Studies on the Sequential and Parallel Complexity of Computer Algebra Problems
Directorate for Computer & Information Science & Engineering
grant June 15, 1985 - November 30, 1987
Complexity Studies in Computer Algebra (Computer Research)
Directorate for Computer & Information Science & Engineering

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