Erich Kaltofen

Computing Approximate Greatest Common Right Divisors of Differential Polynomials

Foundations of Computational Mathematics.

Elimination-based certificates for triangular equivalence and rank profiles

JOURNAL OF SYMBOLIC COMPUTATION, Vol. 98, pp. 246–269.

Sparse Polynomial Interpolation With Arbitrary Orthogonal Polynomial Bases

ISSAC'18: PROCEEDINGS OF THE 2018 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, 223–230.

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. Presented at the the 2017 ACM.

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. Presented at the the 2017 ACM.

Linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix

Proceedings of the 2016 ACM International Symposium on Symbolic and Algebraic Computation (ISSAC 2016), 199–206.

Numerical Sparsity Determination and Early Termination

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '16. Presented at the the ACM.

Sparse multivariate function recovery with a small number of evaluations

Journal of Symbolic Computation, 75, 209–218.

Error-Correcting Sparse Interpolation in the Chebyshev Basis

Proceedings of the 2015 ACM on International Symposium on Symbolic and Algebraic Computation - ISSAC '15. Presented at the the 2015 ACM.

Cleaning-up data for sparse model synthesis

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

Essentially optimal interactive certificates in linear algebra

Proceedings of the 39th International Symposium on Symbolic and Algebraic Computation - ISSAC '14. Presented at the the 39th International Symposium.

Numerical linear system solving with parametric entries by error correction

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

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

In Computer Mathematics (pp. 183–197).

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. Presented at the the 39th International Symposium.

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. Presented at the the 39th International Symposium.

Symbolic Computation and Complexity Theory Transcript of My Talk

In Computer Mathematics (pp. 3–7).

A fraction free Matrix Berlekamp/Massey algorithm

Linear Algebra and Its Applications, 439(9), 2515–2526.

On the matrix berlekamp-massey algorithm

ACM Transactions on Algorithms, 9(4).

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. Presented at the the 38th international symposium.

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. Presented at the the 37th International Symposium.

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

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

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

Journal of Symbolic Computation, 47(4), 480–491.

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. Presented at the the 37th International Symposium.

Special issue on symbolic and algebraic computation foundations, algorithmics and applications: ISSAC 2009

Journal of Symbolic Computation, 47(7), 751–751.

Fast estimates of Hankel matrix condition numbers and numeric sparse interpolation

Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation - SNC '11. Presented at the the 2011 International Workshop.

Quadratic-time certificates in linear algebra

Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11. Presented at the the 36th international symposium.

Supersparse black box rational function interpolation

Proceedings of the 36th international symposium on Symbolic and algebraic computation - ISSAC '11. Presented at the the 36th international symposium.

Symmetric determinantal representation of formulas and weakly skew circuits

The “Seven Dwarfs” of Symbolic Computation

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

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. Presented at the the 2010 International Symposium.

Efficiently certifying non-integer powers

Computational Complexity, 19(3), 355–366.

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. Presented at the the 4th International Workshop.

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. Presented at the the 2009 conference.

Approximate factorization of multivariate polynomials using singular value decomposition

Journal of Symbolic Computation, 43(5), 359–376.

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. Presented at the the twenty-first international symposium.

Expressing a fraction of two determinants as a determinant

Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08. Presented at the the twenty-first international symposium.

Irreducible polynomials and barker sequences

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

On exact and approximate interpolation of sparse rational functions

ISSAC 2007: International Symposium for Symbolic and Algebraic Computation: Proceedings.

On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms

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

Structured Low Rank Approximation of a Sylvester Matrix

In Trends in Mathematics (pp. 69–83).

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. Presented at the the 2006 international symposium.

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. Presented at the the 2006 international symposium.

Hybrid symbolic-numeric computation

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

Generic matrix multiplication and memory management in linBox

Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05. Presented at the the 2005 international symposium.

On the complexity of computing determinants

Computational Complexity, 13, 91–130.

On the complexity of factoring bivariate supersparse (Lacunary) polynomials

Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC '05. Presented at the the 2005 international symposium.

Approximate factorization of multivariate polynomials via differential equations

Proceedings of the 2004 international symposium on Symbolic and algebraic computation - ISSAC '04. Presented at the the 2004 international symposium.

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

Journal of Computational and Applied Mathematics, 162(1), 133–146.

Deterministic distinct-degree factorization of polynomials over finite fields

Journal of Symbolic Computation, 38(6), 1461–1470.

Absolute factorization of polynomials

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

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

Journal of Symbolic Computation, 36(04-Mar), 401–424.

Computer algebra - impact on research

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

Computer algebra handbook foundations, applications, systems

Early termination in sparse interpolation algorithms

Journal of Symbolic Computation, 36(04-Mar), 365–400.

FoxBox and other blackbox systems

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

Hybrid methods

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

Linear systems

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

On approximate irreducibility of polynomials in several variables

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

Polynomial factorization

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

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. Presented at the the 2002 international symposium.

Efficient matrix preconditioners for black box linear algebra

Linear Algebra and Its Applications, 343(2002 Mar 1), 119–146.

LINBOX: A GENERIC LIBRARY FOR EXACT LINEAR ALGEBRA

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

Challenges of symbolic computation: My favorite open problems

Journal of Symbolic Computation, 29(6), 891–919.

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. Presented at the the 2000 international symposium.

Distributed matrix-free solution of large sparse linear systems over finite fields

Algorithmica, 24(3-4), 331–348.

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.

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.

Symbolic computation in Java

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

Efficient algorithms for computing the nearest polynomial with constrained roots

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

FOXBOX

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

Subquadratic-time factoring of polynomials over finite fields

Mathematics of Computation, 67(223), 1179–1197.

Fast polynomial factorization over high algebraic extensions of finite fields

Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97. Presented at the the 1997 international symposium.

On randomized Lanczos algorithms

Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97. Presented at the the 1997 international symposium.

Teaching computational abstract algebra

Journal of Symbolic Computation, 23(5-6), 503–515.

Generic Gram-Schmidt orthogonalization by exact division

Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96. Presented at the the 1996 international symposium.

On rank properties of Toeplitz matrices over finite fields

Proceedings of the 1996 international symposium on Symbolic and algebraic computation - ISSAC '96. Presented at the the 1996 international symposium.

Prediction Based Task Scheduling in Distributed Computing

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

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

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

Effective Noether Irreducibility Forms and Applications

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

Integer division in residue number systems

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

Process Scheduling in DSC and the Large Sparse Linear Systems Challenge

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

A Distributed Approach to Problem Solving in Maple

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

Asymptotically fast solution of Toeplitz-like singular linear systems

Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94. Presented at the the international symposium.

Factoring high-degree polynomials by the black box Berlekamp algorithm

Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '94. Presented at the the international symposium.

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

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

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

ACM SIGSAM Bulletin, 27(4), 2.

On computing determinants of matrices without divisions

Papers from the international symposium on Symbolic and algebraic computation - ISSAC '92. Presented at the Papers from the international symposium.

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

Proceedings., 33rd Annual Symposium on Foundations of Computer Science. Presented at the Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

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.

On fast multiplication of polynomials over arbitrary algebras

Acta Informatica, 28(7), 693–701.

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. Presented at the the third annual ACM symposium.

Computing the irreducible real factors and components of an algebraic curve

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

Modular rational sparse multivariate polynomial interpolation

Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '90. Presented at the the international symposium.

An improved Las Vegas primality test

Proceedings of the ACM-SIGSAM 1989 international symposium on Symbolic and algebraic computation - ISSAC '89. Presented at the the ACM-SIGSAM 1989 international symposium.

Computing greatest common divisors and factorizations in quadratic number fields

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

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

In Lecture Notes in Computer Science (pp. 317–322).

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

ACM SIGSAM Bulletin, 22(2), 41–49.

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. Presented at the [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

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

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

Efficient Parallel Evaluation of Straight-Line Code and Arithmetic Circuits

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

Greatest common divisors of polynomials given by straight-line programs

Journal of the ACM, 35(1), 231–264.

Computer Algebra Algorithms

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

Deterministic irreducibility testing of polynomials over large finite fields

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

Fast Parallel Computation of Hermite and Smith Forms of Polynomial Matrices

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

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. Presented at the the nineteenth annual ACM conference.

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.

Efficient parallel evaluation of straight-line code and arithmetic circuits

In VLSI Algorithms and Architectures (pp. 236–245).

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.

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.

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. Presented at the the seventeenth annual ACM symposium.

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

26th Annual Symposium on Foundations of Computer Science (sfcs 1985). Presented at the 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

Effective Hilbert irreducibility

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

Factoring sparse multivariate polynomials

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

Fast parallel absolute irreducibility testing

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

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

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

Sparse hensel lifting

In EUROCAL '85 (pp. 4–17).

A Generalized Class of Polynomials that are Hard to Factor

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

On the complexity of finding short vectors in integer lattices

In Lecture Notes in Computer Science (pp. 236–244).

A polynomial reduction from multivariate to bivariate integral polynomial factorization.

Proceedings of the fourteenth annual ACM symposium on Theory of computing - STOC '82. Presented at the the fourteenth annual ACM symposium.

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

23rd Annual Symposium on Foundations of Computer Science (sfcs 1982). Presented at the 23rd Annual Symposium on Foundations of Computer Science.

A generalized class of polynomials that are hard to factor

Proceedings of the fourth ACM symposium on Symbolic and algebraic computation - SYMSAC '81. Presented at the the fourth ACM symposium.