E. Kaltofen

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Fast parallel computation of hermite and smith forms of polynomial matrices

B. D. Saunders, E. Kaltofen, M. Krishnamoorthy, 1987 .

Factorization of multivariate polynomials over finite fields

J. Gathen, E. Kaltofen, 1985 .

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

E. Kaltofen, N. Yui, 1991 .

Cited References

E. Kaltofen, V. Weispfenning, J. Grabmeier, 2003 .

On the complexity of factoring polynomials with integer coefficients

Erich Kaltofen, E. Kaltofen, 1982 .

Factorization of Polynomials

Erich Kaltofen, E. Kaltofen, 1983 .

Computer Algebra Algorithms

E. Kaltofen, 1987 .

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

E. Kaltofen, 1995 .

The “Seven Dwarfs” of Symbolic Computation

E. Kaltofen, 2012 .

Structured Low Rank Approximation of a Sylvester Matrix

E. Kaltofen, L. Zhi, Zhengfeng Yang, 2007 .

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

Erich Kaltofen, Zhengfeng Yang, Lihong Zhi, 2006, ISSAC '06.

Exact Certification in Global Polynomial Optimization Via Rationalizing Sums-Of-Squares

E. Kaltofen, 2009 .

CHALLENGES IN LINEAR AND POLYNOMIAL ALGEBRA IN SYMBOLIC COMPUTATION SOFTWARE

E. Kaltofen, S. Watt, W. Decker, 2005 .

Efficient matrix preconditioners for black box linear algebra

B. D. Saunders, E. Kaltofen, W. Eberly, 2002 .

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

Bin Li, Erich Kaltofen, Zhengfeng Yang, 2008, ISSAC '08.

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

E. Kaltofen, G. Villard, 2004 .

Black box linear algebra with the linbox library

Erich Kaltofen, William J. Turner, E. Kaltofen, 2002 .

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

Erich Kaltofen, Austin Lobo, E. Kaltofen, 1999, Algorithmica.

1 Major Research Results 1 . 1 Polynomial Factorization

E. Kaltofen, E. Imamoglu, 1999 .

Berlekamp/massey algorithms for linearly generated matrix sequences

Erich Kaltofen, George Yuhasz, E. Kaltofen, 2009 .

ON THE COMPLEXITY OF COMPUTING DETERMINANTS* (Extended abstract)

E. Kaltofen, G. Villard, 2001 .

Parallel Algebraic Algorithm Design

E. Kaltofen, 1989 .

Algebraic Algorithms 1

V. Pan, E. Kaltofen, A. D. az, 1997 .

Gerhard Hiss Algorithms of Representation Theory

E. Kaltofen, G. Hiss, J. Grabmeier, 2022 .

Size Efficient Parallel Algebraic Circuits for Partial Derivatives *

E. Kaltofen, M. Singer, 2008 .

Computer Algebra Handbook : Foundations · Applications · Systems

Erich Kaltofen, Volker Weispfenning, Johannes Grabmeier, 2003 .

Cited References

E. Kaltofen, V. Weispfenning, J. Grabmeier, 2019, Effective Project Management.

Greatest Common Divisors and Factorizations in Quadratic Number Fields

E. Kaltofen, Heinrich, Rolletschek, 2010 .

Effective Noether Irreducibility Forms and Applications (Extended Abstract)

E. Kaltofen, 1991, STOC.

Challenges in Symbolic Computation Software, 02.07. - 07.07.2006

Stephen M. Watt, Erich Kaltofen, Mike Dewar, 2006, Challenges in Symbolic Computation Software.

Factorization of Polynomials

E. Kaltofen, 1983 .

Factoring Sparse Multivariate Polynomials

Joachim von zur Gathen, J. Gathen, E. Kaltofen, 1983, J. Comput. Syst. Sci..

Computer algebra handbook

Erich Kaltofen, Volker Weispfenning, Johannes Grabmeier, 2002 .

Proceedings of the third conference on Computers and mathematics

Stephen M. Watt, Erich Kaltofen, E. Kaltofen, 1989 .

Parallel Algebraic Design*

E. Kaltofen, 2022 .

Proceedings of the 2001 International Symposium on Symbolic and Algebraic Computation, ISSAC 2001, ORCCA & University of Western Ontario, London, Ontario, Canada, July 22-25, 2001

Erich Kaltofen, Gilles Villard, E. Kaltofen, 2001, ISSAC.

Polynomial Factorization 1982–1986

E. Kaltofen, 2020, Computers in Mathematics.

Symmetric Determinantal Representation of Weakly-Skew Circuits

Erich Kaltofen, Bruno Grenet, Pascal Koiran, 2011, STACS.

Symmetric Determinantal Representation of Formulas and Weakly Skew Circuits pdf

Erich Kaltofen, Bruno Grenet, Pascal Koiran, 2010, ArXiv.

Solving systems of nonlinear polynomial equations faster

Erich Kaltofen, John F. Canny, Y. N. Lakshman, 1989, ISSAC '89.

On the matrix berlekamp-massey algorithm

Erich Kaltofen, George Yuhasz, E. Kaltofen, 2013, TALG.

On the complexity of computing determinants

Erich Kaltofen, Gilles Villard, E. Kaltofen, 2001, computational complexity.

Symbolic Computation and Complexity Theory Transcript of My Talk

Erich Kaltofen, E. Kaltofen, 2012, ASCM.

On fast multiplication of polynomials over arbitrary algebras

Erich Kaltofen, David G. Cantor, D. Cantor, 1991, Acta Informatica.

Subquadratic-time factoring of polynomials over finite fields

Erich Kaltofen, Victor Shoup, V. Shoup, 1995, STOC '95.

Computing greatest common divisors and factorizations in quadratic number fields

Erich Kaltofen, Heinrich Rolletschek, H. Rolletschek, 1989 .

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

Erich Kaltofen, Markus A. Hitz, Y. N. Lakshman, 1999, ISSAC '99.

Efficient algorithms for computing the nearest polynomial with constrained roots

Erich Kaltofen, Markus A. Hitz, E. Kaltofen, 1998, ISSAC '98.

A generalized class of polynomials that are hard to factor

Erich Kaltofen, David R. Musser, B. David Saunders, 1981, SYMSAC '81.

LINBOX: A GENERIC LIBRARY FOR EXACT LINEAR ALGEBRA

Erich Kaltofen, Jean-Guillaume Dumas, Gilles Villard, 2002 .

Polynomial-Time Factorization of Multivariate Polynomials over Finite Fields

Erich Kaltofen, Joachim von zur Gathen, J. Gathen, 1983, ICALP.

Factorization of Polynomials

E. Kaltofen, E Kaltofen, 1983 .

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

Erich Kaltofen, E. Kaltofen, 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

A polynomial reduction from multivariate to bivariate integral polynomial factorization.

Erich Kaltofen, E. Kaltofen, 1982, STOC '82.

Hermite Rational Function Interpolation with Error Correction

Clément Pernet, Zhi-Hong Yang, Erich L. Kaltofen, 2020, CASC.

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

Erich Kaltofen, Lihong Zhi, Feng Guo, 2012, ISSAC.

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

Erich Kaltofen, Zhengfeng Yang, Lihong Zhi, 2009, SNC '09.

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

Erich Kaltofen, Angel Díaz, E. Kaltofen, 1998, ISSAC '98.

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

Bin Li, Erich Kaltofen, Zhengfeng Yang, 2012, J. Symb. Comput..

Fast estimates of Hankel matrix condition numbers and numeric sparse interpolation

Erich Kaltofen, Zhengfeng Yang, Wen-shin Lee, 2012, SNC '11.

Computing Approximate Greatest Common Right Divisors of Differential Polynomials

E. Kaltofen, M. Giesbrecht, Joseph Haraldson, 2019, Foundations of Computational Mathematics.

Computing Approximate Greatest Common Right Divisors of Differential Polynomials

Erich Kaltofen, Mark Giesbrecht, Joseph Haraldson, 2017, Found. Comput. Math..

Challenges of Symbolic Computation: My Favorite Open Problems

Erich Kaltofen, E. Kaltofen, 2000, J. Symb. Comput..

Integer Division in Residue Number Systems

Erich Kaltofen, Markus A. Hitz, E. Kaltofen, 1995, IEEE Trans. Computers.

Algebraic Algorithms

Victor Y. Pan, Erich Kaltofen, Elias P. Tsigaridas, 1999, Computing Handbook, 3rd ed..

Computing Handbook (third Edition) Volume I: Computer Science and Software Engineering

V. Pan, J. Díaz-Herrera, E. Kaltofen, 2013 .

Challenges of Symbolic Computation

E. Kaltofen, 2000 .

Effective Noether irreducibility forms and applications

Erich Kaltofen, E. Kaltofen, 1991, STOC '91.

Computing the irreducible real factors and components of an algebraic curve

Erich Kaltofen, E. Kaltofen, 1989, SCG '89.

Fifteen years after DSC and WLSS2 what parallel computations I do today: invited lecture at PASCO 2010

Erich Kaltofen, E. Kaltofen, 2010, PASCO.

On rank properties of Toeplitz matrices over finite fields

Erich Kaltofen, Austin Lobo, E. Kaltofen, 1996, ISSAC '96.

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

Victor Y. Pan, Erich Kaltofen, V. Pan, 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.

Processor efficient parallel solution of linear systems over an abstract field

Victor Y. Pan, Erich Kaltofen, V. Pan, 1991, SPAA '91.

Fast parallel algorithms for similarity of matrices

Erich Kaltofen, B. David Saunders, B. D. Saunders, 1986, SYMSAC '86.

Fast Parallel Absolute Irreducibility Testing

Erich Kaltofen, E. Kaltofen, 1985, J. Symb. Comput..

Factoring Sparse Multivariate Polynomials

Erich Kaltofen, Joachim von zur Gathen, J. Gathen, 1983, J. Comput. Syst. Sci..

Parallel Solution of Toeplitz and Toeplitz-Like Linear Systems Over Fields of Small Positive Characteristic

Victor Y. Pan, Erich Kaltofen, V. Pan, 1994, PASCO.

Deterministic distinct-degree factorization of polynomials over finite fields

Erich Kaltofen, Shuhong Gao, Alan G. B. Lauder, 2004, J. Symb. Comput..

Fast polynomial factorization over high algebraic extensions of finite fields

Erich Kaltofen, Victor Shoup, V. Shoup, 1997, ISSAC.

Expressing a fraction of two determinants as a determinant

Erich Kaltofen, Pascal Koiran, P. Koiran, 2008, ISSAC '08.

On exact and approximate interpolation of sparse rational functions

Erich Kaltofen, Zhengfeng Yang, E. Kaltofen, 2007, ISSAC '07.

On the complexity of factoring bivariate supersparse (Lacunary) polynomials

Erich Kaltofen, Pascal Koiran, P. Koiran, 2005, ISSAC.

Polynomial factorization: a success story

Erich Kaltofen, E. Kaltofen, 2003, ISSAC '03.

Qualifying Examination Topics August 2007 Computer Algebra (MA 522-MA792K)

Erich Kaltofen, E. Kaltofen, 2007 .

Computing the smith forms of integer matrices and solving related problems

B. David Saunders, B. D. Saunders, Zhendong Wan, 2005 .

Preface Conference Organization Conference Chairs Program Chairs Program Committee Invited Speakers Tutorial Speakers Local Organization External Reviewers Structural Alignments of Rna Sequences

Robert H. Lewis, B. Buchberger, D. Tominaga, 2008 .

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

Erich Kaltofen, Jean-Guillaume Dumas, Gilles Villard, 2016, ISSAC.

Cited References

E. Kaltofen, V. Weispfenning, J. Grabmeier, 2003 .

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

Erich Kaltofen, Wen-shin Lee, Austin Lobo, 2000, ISSAC.

On randomized Lanczos algorithms

Erich Kaltofen, Wayne Eberly, E. Kaltofen, 1997, ISSAC.

Generic Gram-Schmidt orthogonalization by exact division

Úlfar Erlingsson, Erich Kaltofen, David R. Musser, 1996, ISSAC '96.

Process Scheduling in DSC and the Large Sparse Linear Systems Challenge

Erich Kaltofen, Markus A. Hitz, Thomas Valente, 1993, DISCO.

Analysis of Coppersmith's Block Wiedemann Algorithm for the Parallel Solution of Sparse Linear Systems

Erich Kaltofen, E. Kaltofen, 1993, AAECC.

On computing determinants of matrices without divisions

Erich Kaltofen, E. Kaltofen, 1992, ISSAC '92.

Polynomial Factorization 1987-1991

Erich Kaltofen, E. Kaltofen, 1992, LATIN.

On Wiedemann's Method of Solving Sparse Linear Systems

Erich Kaltofen, B. David Saunders, B. D. Saunders, 1991, AAECC.

Parallel algorithms for matrix normal forms

Erich Kaltofen, B. David Saunders, B. D. Saunders, 1990 .

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

Erich Kaltofen, Barry M. Trager, E. Kaltofen, 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

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

Erich Kaltofen, Y. N. Lakshman, Yagati N. Lakshman, 1988, TOMS.

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

Erich Kaltofen, E. Kaltofen, 1985, SIAM J. Comput..

Computational algebraic complexity

Erich Kaltofen, E. Kaltofen, 1990 .

Factorization of Polynomials Given by Straight-Line Programs

Erich Kaltofen, E. Kaltofen, 1989, Adv. Comput. Res..

Greatest common divisors of polynomials given by straight-line programs

Erich Kaltofen, E. Kaltofen, 1988, JACM.

Factorization of Polynomials

E. Kaltofen, 1983 .

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

Zhi-Hong Yang, Erich L. Kaltofen, E. Kaltofen, 2019, IEEE Transactions on Information Theory.

Computers and Mathematics

E. Kaltofen, 1989, Springer US.

Efficient matrix preconditioners for black box linear algebra

B. D. Saunders, E. Kaltofen, W. Eberly, 2002 .

Factoring high-degree polynomials by the black box Berlekamp algorithm

Erich Kaltofen, Austin Lobo, E. Kaltofen, 1994, ISSAC '94.

Teaching Computational Abstract Algebra

Erich Kaltofen, E. Kaltofen, 1997, J. Symb. Comput..

Uniform closure properties of P-computable functions

Erich Kaltofen, E. Kaltofen, 1986, STOC '86.

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

Erich Kaltofen, E. Kaltofen, 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

Arithmetic in Quadratic Fields with Unique Factorization

Erich Kaltofen, Heinrich Rolletschek, H. Rolletschek, 1985, European Conference on Computer Algebra.

Effective Hilbert Irreducibility

Erich Kaltofen, E. Kaltofen, 1984, Inf. Control..

On the complexity of finding short vectors in integer lattices

Erich Kaltofen, E. Kaltofen, 1983, EUROCAL.

Foreword

Erich Kaltofen, E. Kaltofen, 2021, J. Symb. Comput..

Efficient Parallel Evaluation of Straight-Line Code and Arithmetic Circuits

Gary L. Miller, Erich Kaltofen, Vijaya Ramachandran, 1986, SIAM J. Comput..

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

E. Kaltofen, 2002, ISSAC '02.

Elimination-based certificates for triangular equivalence and rank profiles

Erich Kaltofen, Jean-Guillaume Dumas, Clément Pernet, 2019, J. Symb. Comput..

Interactive certificate for the verification of Wiedemann's Krylov sequence: application to the certification of the determinant, the minimal and the characteristic polynomials of sparse matrices pdf

Erich Kaltofen, Jean-Guillaume Dumas, Emmanuel Thomé, 2015, ArXiv.

On computing the degree of a Chebyshev Polynomial from its value

Erich L. Kaltofen, Erdal Imamoglu, E. Kaltofen, 2021, J. Symb. Comput..

Sparse Polynomial Interpolation With Arbitrary Orthogonal Polynomial Bases

Erich Kaltofen, Zhengfeng Yang, Erdal Imamoglu, 2018, ISSAC.

Supersparse black box rational function interpolation

Erich Kaltofen, Michael Nehring, E. Kaltofen, 2011, ISSAC '11.

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

Erich Kaltofen, Clément Pernet, E. Kaltofen, 2014, ISSAC.

Approximate factorization of multivariate polynomials using singular value decomposition

Erich Kaltofen, Zhengfeng Yang, Lihong Zhi, 2008, J. Symb. Comput..

Approximate factorization of multivariate polynomials via differential equations

Erich Kaltofen, Zhengfeng Yang, Lihong Zhi, 2004, ISSAC '04.

Explicit Construction of the Hilbert Class Fields of Imaginary Quadratic Fields with Class Numbers 7 and 11

Erich Kaltofen, Noriko Yui, E. Kaltofen, 1984, EUROSAM.

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

Erich Kaltofen, Michael F. Singer, Hoon Hong, 1999, SIGS.

Computing Higher Polynomial Discriminants

Erich Kaltofen, E. Kaltofen, 2021, ISSAC.

Deterministic Irreducibility Testing of Polynomials over Large Finite Fields

Erich Kaltofen, E. Kaltofen, 1987, J. Symb. Comput..

Polynomial Factorization 1982–1986

E. Kaltofen, 2020, Computers in Mathematics.

An improved Las Vegas primality test

Erich Kaltofen, Thomas Valente, Norika Yui, 1989, ISSAC '89.