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2019 journal article
Computing Approximate Greatest Common Right Divisors of Differential Polynomials
Foundations of Computational Mathematics.
2019 article
Elimination-based certificates for triangular equivalence and rank profiles
JOURNAL OF SYMBOLIC COMPUTATION, Vol. 98, pp. 246–269.
2018 conference paper
Sparse Polynomial Interpolation With Arbitrary Orthogonal Polynomial Bases
ISSAC'18: PROCEEDINGS OF THE 2018 ACM INTERNATIONAL SYMPOSIUM ON SYMBOLIC AND ALGEBRAIC COMPUTATION, 223–230.
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. Presented at the the 2017 ACM.
Event: the 2017 ACM
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. Presented at the the 2017 ACM.
Event: the 2017 ACM
2016 conference paper
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.
2016 conference paper
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.
Event: the ACM
2016 journal article
Sparse multivariate function recovery with a small number of evaluations
Journal of Symbolic Computation, 75, 209–218.
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. Presented at the the 2015 ACM.
Event: the 2015 ACM
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.
Event: the 2014 Symposium
2014 conference paper
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.
Event: the 39th International Symposium
2014 conference paper
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.
Event: the 2014 Symposium
2014 chapter
Sparse Polynomial Interpolation by Variable Shift in the Presence of Noise and Outliers in the Evaluations
In Computer Mathematics (pp. 183–197).
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. Presented at the the 39th International Symposium.
Event: the 39th International Symposium
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. Presented at the the 39th International Symposium.
Event: the 39th International Symposium
2014 chapter
Symbolic Computation and Complexity Theory Transcript of My Talk
In Computer Mathematics (pp. 3–7).
2013 journal article
A fraction free Matrix Berlekamp/Massey algorithm
Linear Algebra and Its Applications, 439(9), 2515–2526.
2013 journal article
On the matrix berlekamp-massey algorithm
ACM Transactions on Algorithms, 9(4).
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. Presented at the the 38th international symposium.
Event: the 38th international symposium
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. Presented at the the 37th International Symposium.
Event: the 37th International Symposium
2012 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.
2012 journal article
On the Berlekamp/Massey algorithm and counting singular Hankel matrices over a finite field
Journal of Symbolic Computation, 47(4), 480–491.
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. Presented at the the 37th International Symposium.
Event: the 37th International Symposium
2012 journal article
Special issue on symbolic and algebraic computation foundations, algorithmics and applications: ISSAC 2009
Journal of Symbolic Computation, 47(7), 751–751.
2011 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. Presented at the the 2011 International Workshop.
Event: the 2011 International Workshop
2011 conference paper
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.
Event: the 36th international symposium
2011 conference paper
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.
Event: the 36th international symposium
2011 other
Symmetric determinantal representation of formulas and weakly skew circuits
2011 chapter
The “Seven Dwarfs” of Symbolic Computation
In Texts & Monographs in Symbolic Computation (pp. 95–104).
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. Presented at the the 2010 International Symposium.
Event: the 2010 International Symposium
2010 journal article
Efficiently certifying non-integer powers
Computational Complexity, 19(3), 355–366.
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. Presented at the the 4th International Workshop.
Event: the 4th International Workshop
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. Presented at the the 2009 conference.
Event: the 2009 conference
2008 journal article
Approximate factorization of multivariate polynomials using singular value decomposition
Journal of Symbolic Computation, 43(5), 359–376.
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. Presented at the the twenty-first international symposium.
Event: the twenty-first international symposium
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. Presented at the the twenty-first international symposium.
Event: the twenty-first international symposium
2007 journal article
Irreducible polynomials and barker sequences
ACM Communications in Computer Algebra, 41(4), 118.
2007 conference paper
On exact and approximate interpolation of sparse rational functions
ISSAC 2007: International Symposium for Symbolic and Algebraic Computation: Proceedings.
2007 conference paper
On probabilistic analysis of randomization in hybrid symbolic-numeric algorithms
International Workshop on Symbolic-Numeric Computation: Proceedings. New York: ACM Press.
2007 chapter
Structured Low Rank Approximation of a Sylvester Matrix
In Trends in Mathematics (pp. 69–83).
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. Presented at the the 2006 international symposium.
Event: the 2006 international symposium
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. Presented at the the 2006 international symposium.
Event: the 2006 international symposium
2006 conference paper
Hybrid symbolic-numeric computation
Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06. Presented at the the 2006 international symposium.
Event: the 2006 international symposium
2005 conference paper
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.
Event: the 2005 international symposium
2005 journal article
On the complexity of computing determinants
Computational Complexity, 13, 91–130.
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. Presented at the the 2005 international symposium.
Event: the 2005 international symposium
2004 conference paper
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.
Event: the 2004 international symposium
2004 journal article
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.
2004 journal article
Deterministic distinct-degree factorization of polynomials over finite fields
Journal of Symbolic Computation, 38(6), 1461–1470.
2003 chapter
Absolute factorization of polynomials
In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), Computer Algebra Handbook (p. 26). Heidelberg, Germany: Springer Verlag.
Ed(s): J. Grabmeier, & V. Weispfenning
2003 journal article
Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases
Journal of Symbolic Computation, 36(04-Mar), 401–424.
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.
Ed(s): J. Grabmeier, & V. Weispfenning
2003 book
Computer algebra handbook foundations, applications, systems
2003 journal article
Early termination in sparse interpolation algorithms
Journal of Symbolic Computation, 36(04-Mar), 365–400.
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.
Ed(s): J. Grabmeier, & V. Weispfenning
2003 chapter
Hybrid methods
In J. Grabmeier, E. Kaltofen, & V. Weispfenning (Eds.), Computer Algebra Handbook (pp. 112–125). Heidelberg, Germany: Springer Verlag.
Ed(s): J. Grabmeier, & V. Weispfenning
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.
Ed(s): J. Grabmeier, & V. Weispfenning
2003 conference paper
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.
Event: the 2003 international symposium
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.
Event: the 2003 international symposium
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. Presented at the the 2002 international symposium.
Event: the 2002 international symposium
2002 journal article
Efficient matrix preconditioners for black box linear algebra
Linear Algebra and Its Applications, 343(2002 Mar 1), 119–146.
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.
Event: Proceedings of the First International Congress of Mathematical Software
2000 journal article
Challenges of symbolic computation: My favorite open problems
Journal of Symbolic Computation, 29(6), 891–919.
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. Presented at the the 2000 international symposium.
Event: the 2000 international symposium
1999 journal article
Distributed matrix-free solution of large sparse linear systems over finite fields
Algorithmica, 24(3-4), 331–348.
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.
Event: the 1999 international symposium
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.
Event: the 1999 international symposium
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.
Event: the 1999 international symposium
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. Presented at the the 1998 international symposium.
Event: the 1998 international symposium
1998 conference paper
FOXBOX
Proceedings of the 1998 international symposium on Symbolic and algebraic computation - ISSAC '98. Presented at the the 1998 international symposium.
Event: the 1998 international symposium
1998 journal article
Subquadratic-time factoring of polynomials over finite fields
Mathematics of Computation, 67(223), 1179–1197.
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. Presented at the the 1997 international symposium.
Event: the 1997 international symposium
1997 conference paper
On randomized Lanczos algorithms
Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC '97. Presented at the the 1997 international symposium.
Event: the 1997 international symposium
1997 journal article
Teaching computational abstract algebra
Journal of Symbolic Computation, 23(5-6), 503–515.
1996 conference paper
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.
Event: the 1996 international symposium
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. Presented at the the 1996 international symposium.
Event: the 1996 international symposium
1996 chapter
Prediction Based Task Scheduling in Distributed Computing
In Languages, Compilers and Run-Time Systems for Scalable Computers (pp. 317–320).
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.
1995 journal article
Effective Noether Irreducibility Forms and Applications
Journal of Computer and System Sciences, 50(2), 274–295.
1995 journal article
Integer division in residue number systems
IEEE Transactions on Computers, 44(8), 983–989.
1995 journal article
Process Scheduling in DSC and the Large Sparse Linear Systems Challenge
Journal of Symbolic Computation, 19(1-3), 269–282.
1994 chapter
A Distributed Approach to Problem Solving in Maple
In Maple V: Mathematics and its Applications (pp. 13–21).
1994 conference paper
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.
Event: the international symposium
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. Presented at the the international symposium.
Event: the international symposium
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 (pp. 195–212).
1993 journal article
Direct proof of a theorem by Kalkbrener, Sweedler, and Taylor
ACM SIGSAM Bulletin, 27(4), 2.
1992 conference paper
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.
Event: Papers from the international symposium
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. Presented at the Proceedings., 33rd Annual Symposium on Foundations of Computer Science.
Event: Proceedings., 33rd Annual Symposium on Foundations of Computer Science
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.
Event: the twenty-third annual ACM symposium
1991 journal article
On fast multiplication of polynomials over arbitrary algebras
Acta Informatica, 28(7), 693–701.
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. Presented at the the third annual ACM symposium.
Event: the third annual ACM symposium
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.
1990 conference paper
Modular rational sparse multivariate polynomial interpolation
Proceedings of the international symposium on Symbolic and algebraic computation - ISSAC '90. Presented at the the international symposium.
Event: the international symposium
1989 conference paper
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.
Event: the ACM-SIGSAM 1989 international symposium
1989 journal article
Computing greatest common divisors and factorizations in quadratic number fields
Mathematics of Computation, 53(188), 697–697.
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 (pp. 317–322).
1988 journal article
Analysis of the binary complexity of asymptotically fast algorithms for linear system solving
ACM SIGSAM Bulletin, 22(2), 41–49.
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. Presented at the [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.
Event: [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
1988 journal article
Dagwood: a system for manipulating polynomials given by straight-line programs
ACM Transactions on Mathematical Software, 14(3), 218–240.
1988 journal article
Efficient Parallel Evaluation of Straight-Line Code and Arithmetic Circuits
SIAM Journal on Computing, 17(4), 687–695.
1988 journal article
Greatest common divisors of polynomials given by straight-line programs
Journal of the ACM, 35(1), 231–264.
1987 journal article
Computer Algebra Algorithms
Annual Review of Computer Science, 2(1), 91–118.
1987 journal article
Deterministic irreducibility testing of polynomials over large finite fields
Journal of Symbolic Computation, 4(1), 77–82.
1987 journal article
Fast Parallel Computation of Hermite and Smith Forms of Polynomial Matrices
SIAM Journal on Algebraic Discrete Methods, 8(4), 683–690.
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. Presented at the the nineteenth annual ACM conference.
Event: the nineteenth annual ACM conference
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.
Event: the fifth ACM symposium
1986 chapter
Efficient parallel evaluation of straight-line code and arithmetic circuits
In VLSI Algorithms and Architectures (pp. 236–245).
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.
Event: the fifth ACM symposium
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.
Event: the eighteenth annual ACM symposium
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. Presented at the the seventeenth annual ACM symposium.
Event: the seventeenth annual ACM symposium
1985 conference paper
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).
Event: 26th Annual Symposium on Foundations of Computer Science (sfcs 1985)
1985 journal article
Effective Hilbert irreducibility
Information and Control, 66(3), 123–137.
1985 journal article
Factoring sparse multivariate polynomials
Journal of Computer and System Sciences, 31(2), 265–287.
1985 journal article
Fast parallel absolute irreducibility testing
Journal of Symbolic Computation, 1(1), 57–67.
1985 journal article
Polynomial-Time Reductions from Multivariate to Bi- and Univariate Integral Polynomial Factorization
SIAM Journal on Computing, 14(2), 469–489.
1985 chapter
Sparse hensel lifting
In EUROCAL '85 (pp. 4–17).
1983 journal article
A Generalized Class of Polynomials that are Hard to Factor
SIAM Journal on Computing, 12(3), 473–483.
1983 chapter
On the complexity of finding short vectors in integer lattices
In Lecture Notes in Computer Science (pp. 236–244).
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. Presented at the the fourteenth annual ACM symposium.
Event: the fourteenth annual ACM symposium
1982 conference paper
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.
Event: 23rd Annual Symposium on Foundations of Computer Science
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. Presented at the the fourth ACM symposium.
Event: the fourth ACM symposium