Edit Profile (opens in new tab) Kaltofen, Erich L. Co-Author Distance Author ID: kaltofen.erich-l Published as: Kaltofen, Erich; Kaltofen, Erich L.; Kaltofen, E. more...less Documents Indexed: 115 Publications since 1981, including 1 Additional arXiv Preprint 6 Contributions as Editor · 1 Further Contribution Co-Authors: 66 Co-Authors with 95 Joint Publications 1,390 Co-Co-Authors all top 5 Co-Authors 27 single-authored 13 Yang, Zhengfeng 11 Zhi, Lihong 8 Saunders, B. David 7 Dumas, Jean-Guillaume 7 Villard, Gilles 6 Pernet, Clément 5 Giesbrecht, Mark W. 5 Koiran, Pascal 5 Lee, Wen-shin 4 Díaz, Angel 4 Hitz, Markus A. 4 von zur Gathen, Joachim 3 Comer, Matthew T. 3 Gao, Shuhong 3 Imamoglu, Erdal 3 Krishnamoorthy, Mukkai S. 3 Lobo, Alberto 3 May, John P. 3 Musser, David R. 3 Shoup, Victor 3 Yuhasz, George 2 Boyer, Brice 2 Eberly, Wayne 2 Grenet, Bruno 2 Li, Bin 2 Lobo, Austin A. 2 Miller, Gary Lee 2 Nehring, Michael 2 Portier, Natacha 2 Ramachandran, Vijaya 2 Rolletschek, Heinrich 2 Turner, William J. 2 Valente, T. 2 Yang, Zhihong 2 Yui, Noriko 1 Ahmadi, Omran 1 Arnold, Andrew 1 Ball, L. Simeon 1 Bernstein, Daniel Julius 1 Blache, Régis 1 Blake, Ian F. 1 Blokhuis, Aart 1 Borwein, Peter Benjamin 1 Cantor, David Geoffrey 1 Carlet, Claude 1 Castro, Francis Noel 1 Chand Gupta, Kishan 1 Charpin, Pascale 1 Chen, Li 1 Cioabă, Sebastian M. 1 Cohen, Stephen D. 1 Colbourn, Charles J. 1 Coulter, Robert S. 1 de Smit, Bart 1 Ding, Jintai 1 Dinitz, Jeffrey H. 1 Doche, Christophe 1 Ebert, Gary Lee 1 Effinger, Gove W. 1 Enge, Andreas 1 Erlingsson, Úlfar 1 Evans, Ronald J. 1 Fan, Haining 1 Fitzgerald, Robert W. 1 Freeman, Timothy S. 1 Fried, Michael David 1 Fu, Lei 1 Garaev, Moubariz Z. 1 Garcia, Arnaldo 1 Gautier, Thierry 1 Giorgi, Pascal 1 Gong, Guang 1 Goss, David Mark 1 Gow, Roderick 1 Grabmeier, Johannes 1 Gregory, Brent 1 Guo, Feng 1 Hachenberger, Dirk 1 Hao, Zhiwei 1 Haraldson, Joseph 1 Hasan, M. Anwar 1 Helleseth, Tor 1 Hinkelmann, Franziska 1 Hirschfeld, James William Peter 1 Hou, Xiang-Dong 1 Hovinen, Bradford 1 Huffman, W. Cary 1 Hutton, Sharon 1 Imirzian, Gregory M. 1 Jacobson, Michael John jun. 1 Jedwab, Jonathan 1 Johnson, Jeremy R. 1 Jungnickel, Dieter 1 Kholosha, Alexander 1 Kyuregyan, Melsik K. 1 Lange, Tanja 1 Laubenbacher, Reinhard C. 1 Lauder, Alan G. B. 1 Lavin, Mark A. 1 Lecerf, Grégoire ...and 47 more Co-Authors all top 5 Serials 16 Journal of Symbolic Computation 4 Mathematics of Computation 3 SIAM Journal on Computing 3 Linear Algebra and its Applications 2 Journal of Computer and System Sciences 2 Computational Complexity 2 ACM Communications in Computer Algebra 1 Acta Informatica 1 IEEE Transactions on Information Theory 1 ACM Transactions on Mathematical Software 1 IEEE Transactions on Computers 1 Information and Control 1 Journal of the Association for Computing Machinery 1 Journal of Computational and Applied Mathematics 1 SIGSAM Bulletin 1 SIAM Journal on Algebraic and Discrete Methods 1 Algorithmica 1 Applicable Algebra in Engineering, Communication and Computing 1 Foundations of Computational Mathematics 1 ACM Transactions on Algorithms 1 Discrete Mathematics and its Applications all top 5 Fields 91 Computer science (68-XX) 51 Numerical analysis (65-XX) 31 Number theory (11-XX) 29 Field theory and polynomials (12-XX) 22 Linear and multilinear algebra; matrix theory (15-XX) 15 Information and communication theory, circuits (94-XX) 14 Commutative algebra (13-XX) 7 General and overarching topics; collections (00-XX) 5 Approximations and expansions (41-XX) 5 Operations research, mathematical programming (90-XX) 3 Algebraic geometry (14-XX) 2 Combinatorics (05-XX) 2 Functions of a complex variable (30-XX) 1 Associative rings and algebras (16-XX) 1 Group theory and generalizations (20-XX) 1 Measure and integration (28-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Special functions (33-XX) 1 Operator theory (47-XX) 1 Calculus of variations and optimal control; optimization (49-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 104 Publications have been cited 1,137 times in 676 Documents Cited by ▼ Year ▼ Handbook of finite fields. Zbl 1319.11001 196 2013 On fast multiplication of polynomials over arbitrary algebras. Zbl 0766.68055 Cantor, David G.; Kaltofen, Erich 114 1991 Subquadratic-time factoring of polynomials over finite fields. Zbl 0902.11053 Kaltofen, Erich; Shoup, Victor 46 1998 Polynomial-time reductions from multivariate to bi- and univariate integral polynomial factorization. Zbl 0605.12001 Kaltofen, Erich 45 1985 Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators. Zbl 0712.12001 Kaltofen, Erich; Trager, Barry M. 39 1990 Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials. Zbl 1356.12011 Kaltofen, Erich; Yang, Zhengfeng; Zhi, Lihong 35 2006 On the complexity of computing determinants. Zbl 1061.68185 Kaltofen, Erich; Villard, Gilles 34 2004 Early termination in sparse interpolation algorithms. Zbl 1074.68080 Kaltofen, Erich; Lee, Wen-shin 30 2003 Fast parallel absolute irreducibility testing. Zbl 0599.68038 Kaltofen, Erich 29 1985 On Wiedemann’s method of solving sparse linear systems. Zbl 0778.65034 Kaltofen, Erich; Saunders, B. David 28 1991 Effective Noether irreducibility forms and applications. Zbl 0844.12006 Kaltofen, Erich 27 1995 Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients. Zbl 1229.90115 Kaltofen, Erich L.; Li, Bin; Yang, Zhengfeng; Zhi, Lihong 27 2012 Factoring sparse multivariate polynomials. Zbl 0599.68037 von zur Gathen, Joachim; Kaltofen, Erich 25 1985 Structures low rank approximation of a Sylvester matrix. Zbl 1117.65060 Kaltofen, Erich; Yang, Zhengfeng; Zhi, Lihong 24 2007 Approximate factorization of multivariate polynomials using singular value decomposition. Zbl 1135.12003 Kaltofen, Erich; May, John P.; Yang, Zhengfeng; Zhi, Lihong 22 2008 Greatest common divisors of polynomials given by straight-line programs. Zbl 0642.68058 Kaltofen, Erich 21 1988 Factorization of multivariate polynomials over finite fields. Zbl 0596.12017 von zur Gathen, Joachim; Kaltofen, Erich 20 1985 Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems. Zbl 0828.65035 Kaltofen, Erich 19 1995 Computer algebra handbook. Foundations, applications, systems. With CD-ROM, demo versions. Zbl 1017.68162 18 2003 Fast parallel computation of Hermite and Smith forms of polynomial matrices. Zbl 0655.65069 Kaltofen, Erich; Krishnamoorthy, M. S.; Saunders, B. David 17 1987 Efficient algorithms for computing the nearest polynomial with constrained roots. Zbl 0917.65045 Hitz, Markus A.; Kaltofen, Erich 17 1998 Sparse Hensel lifting. Zbl 0605.12011 Kaltofen, Erich 17 1985 Polynomial factorization: a success story. Zbl 1068.68709 Kaltofen, Erich 17 2003 Challenges of symbolic computation: My favorite open problems. With an additional open problem by Robert M. Corless and David J. Jeffrey. Zbl 0963.68234 Kaltofen, Erich 16 2000 Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars. Zbl 1493.68402 Kaltofen, Erich; Li, Bin; Yang, Zhengfeng; Zhi, Lihong 16 2008 Approximate factorization of multivariate polynomials via differential equations. Zbl 1134.65346 Gao, Shuhong; Kaltofen, Erich; May, John; Yang, Zhengfeng; Zhi, Lihong 16 2004 Polynomial factorization 1982-1986. Zbl 0773.11078 Kaltofen, Erich 16 1990 Factorization of polynomials. Zbl 0519.68059 Kaltofen, E. 15 1982 Parallel algorithms for matrix normal forms. Zbl 0727.65031 Kaltofen, Erich; Krishnamoorthy, M. S. 14 1990 Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel’s algorithm. Zbl 1326.68358 Kaltofen, Erich; Lee, Wen-shin; Lobo, Austin A. 14 2000 Fast polynomial factorization over high algebraic extensions of finite fields. Zbl 0920.11082 Kaltofen, Erich; Shoup, Victor 13 1997 On rank properties of Toeplitz matrices over finite fields. Zbl 0914.65039 Kaltofen, E.; Lobo, A. 13 1996 On computing determinants of matrices without divisions. Zbl 0978.65502 Kaltofen, Erich 13 1992 On the complexity of factoring bivariate supersparse (lacunary) polynomials. Zbl 1356.11092 Kaltofen, Erich; Koiran, Pascal 12 2005 Efficient parallel evaluation of straight-line code and arithmetic circuits. Zbl 0651.68044 Miller, Gary L.; Ramachandran, Vijaya; Kaltofen, Erich 11 1988 On randomized Lanczos algorithms. Zbl 0917.65025 Eberly, Wayne; Kaltofen, Erich 10 1997 Expressing a fraction of two determinants as a determinant. Zbl 1487.68255 Kaltofen, Erich; Koiran, Pascal 10 2008 Finding small degree factors of multivariate supersparse (lacunary) polynomials over algebraic number fields. Zbl 1356.11093 Kaltofen, Erich; Koiran, Pascal 10 2006 Processor-efficient parallel solution of linear systems. II: The positive characteristic and singular cases. (Extended abstract). Zbl 0977.68879 Kaltofen, Erich; Pan, Victor 9 1992 Efficient matrix preconditioners for black box linear algebra. Zbl 0997.65073 Chen, Li; Eberly, Wayne; Kaltofen, Erich; Saunders, B. David; Turner, William J.; Villard, Gilles 9 2002 Effective Hilbert irreducibility. Zbl 0584.12019 Kaltofen, Erich 9 1985 LinBox: A generic library for exact linear algebra. Zbl 1011.68182 Dumas, J.-G.; Gautier, T.; Giesbrecht, M.; Giorgi, P.; Hovinen, B.; Kaltofen, E.; Saunders, B. D.; Turner, W. J.; Villard, G. 8 2002 FOXBOX: A system for manipulating symbolic objects in black box representation. Zbl 0918.68049 Díaz, Angel; Kaltofen, Erich 8 1998 Asymptotically fast solution of Toeplitz-like singular linear systems. Zbl 0978.15500 Kaltofen, Erich 8 1994 On exact and approximate interpolation of sparse rational functions. Zbl 1190.65019 Kaltofen, Erich; Yang, Zhengfeng 8 2007 On approximate irreducibility of polynomials in several variables. Zbl 1072.68676 Kaltofen, Erich; May, John 8 2003 Deterministic irreducibility testing of polynomials over large finite fields. Zbl 0683.68037 Kaltofen, E. 7 1987 Computing greatest common divisors and factorizations in quadratic number fields. Zbl 0687.12001 Kaltofen, Erich; Rolletschek, Heinrich 7 1989 A generalized class of polynomials that are hard to factor. Zbl 0529.68018 Kaltofen, Erich; Musser, David R.; Saunders, B. David 7 1983 Factoring high-degree polynomials by the black box Berlekamp algorithm. Zbl 0978.68792 Kaltofen, Erich; Lobo, Austin 7 1994 Computing the sign or the value of the determinant of an integer matrix, a complexity survey. Zbl 1037.65044 Kaltofen, Erich; Villard, Gilles 7 2004 On the complexity of computing determinants. (Extended abstract). Zbl 1012.65505 Kaltofen, Erich; Villard, Gilles 7 2001 On the matrix Berlekamp-Massey algorithm. Zbl 1301.65030 Kaltofen, Erich; Yuhasz, George 7 2013 Distributed matrix-free solution of large sparse linear systems over finite fields. Zbl 1078.65542 Kaltofen, E.; Lobo, A. 6 1999 Symmetric determinantal representation of formulas and weakly skew circuits. Zbl 1261.68070 Grenet, Bruno; Kaltofen, Erich L.; Koiran, Pascal; Portier, Natacha 6 2011 Dagwood: A system for manipulating polynomials given by straight-line programs. Zbl 0825.68435 Freeman, Timothy S.; Imirzian, Gregory M.; Kaltofen, Erich; Yagati, Lakshman 6 1988 Efficient parallel evaluation of straight-line code and arithmetic circuits. Zbl 0595.68043 Miller, Gary L.; Ramachandran, Vijaya; Kaltofen, Erich 6 1986 Integer division in residue number systems. Zbl 1053.68501 Hitz, Markus A.; Kaltofen, Erich 6 1995 Mr. Smith goes to Las Vegas: randomized parallel computation of the Smith normal form of polynomial matrices. Zbl 1209.15003 Kaltofen, Erich; Krishnamoorthy, M. S.; Saunders, B. David 5 1989 On computing greatest common divisors with polynomials given by black boxes for their evaluations. Zbl 0919.12007 Díaz, Angel; Kaltofen, Erich 5 1995 Explicit construction of the Hilbert class fields of imaginary quadratic fields with class numbers 7 and 11. Zbl 0583.12007 Kaltofen, Erich; Yui, Noriko 5 1984 Explicit construction of the Hilbert class fields of imaginary quadratic fields by integer lattice reduction. Zbl 0737.11034 Kaltofen, Erich; Yui, Noriko 5 1991 Quadratic-time certificates in linear algebra. Zbl 1323.68607 Kaltofen, Erich L.; Nehring, Michael; Saunders, B. David 5 2011 Subquadratic-time factoring of polynomials over finite fields. Zbl 0921.11068 Kaltofen, Erich; Shoup, Victor 4 1995 Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases. Zbl 1074.68078 Giesbrecht, Mark; Kaltofen, Erich; Lee, Wen-shin 4 2003 Essentially optimal interactive certificates in linear algebra. Zbl 1325.68274 Dumas, Jean-Guillaume; Kaltofen, Erich 4 2014 Sparse polynomial interpolation and Berlekamp/Massey algorithms that correct outlier errors in input values. Zbl 1323.65008 Comer, Matthew T.; Kaltofen, Erich L.; Pernet, Clément 4 2012 Linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix. Zbl 1365.65138 Dumas, Jean-Guillaume; Kaltofen, Erich; Thomé, Emmanuel; Villard, Gilles 4 2016 A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions. Zbl 1356.15002 Kaltofen, Erich; Yang, Zhengfeng; Zhi, Lihong 4 2009 Sparse polynomial interpolation with arbitrary orthogonal polynomial bases. Zbl 1467.41002 Imamoglu, Erdal; Kaltofen, Erich L.; Yang, Zhengfeng 4 2018 Fast estimates of Hankel matrix condition numbers and numeric sparse interpolation. Zbl 1347.65037 Kaltofen, Erich L.; Lee, Wen-shin; Yang, Zhengfeng 4 2011 Error-correcting sparse interpolation in the Chebyshev basis. Zbl 1345.65004 Arnold, Andrew; Kaltofen, Erich L. 4 2015 Deterministic distinct-degree factorization of polynomials over finite fields. Zbl 1130.11336 Gao, Shuhong; Kaltofen, Erich; Lauder, Alan G. B. 3 2005 Polynomial-time factorization of multivariate polynomials over finite fields. Zbl 0526.12002 von zur Gathen, Joachim; Kaltofen, Erich 3 1983 A note on the Risch differential equation. Zbl 0583.68015 Kaltofen, Erich 3 1984 Arithmetic in quadratic fields with unique factorization. Zbl 0596.12001 Kaltofen, Erich; Rolletschek, Heinrich 3 1985 Algorithms for computing the sparsest shifts of polynomials via the Berlekamp/Massey algorithm. Zbl 1072.68669 Giesbrecht, Mark; Kaltofen, Erich; Lee, Wen-shin 3 2002 An output-sensitive variant of the baby steps/giant steps determinant algorithm. Zbl 1072.68675 Kaltofen, Erich 3 2002 Computing the irreducible real factors and components of an algebraic curve. Zbl 0737.14018 Kaltofen, Erich 3 1990 Irreducible polynomials and Barker sequences. Zbl 1322.68271 Borwein, Peter; Kaltofen, Erich; Mossinghoff, Michael J. 3 2007 Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions. Zbl 1323.65068 Guo, Feng; Kaltofen, Erich L.; Zhi, Lihong 3 2012 A fraction free matrix Berlekamp/Massey algorithm. Zbl 1380.16050 Kaltofen, Erich; Yuhasz, George 3 2013 On the complexity of finding short vectors in integer lattices. Zbl 0546.68022 Kaltofen, Erich 2 1983 Second international symposium on parallel symbolic computation, PASCO ’97, Maui, HI, USA, July 20–22, 1997. Zbl 0903.00086 2 1997 Generic Gram-Schmidt orthogonalization by exact division. Zbl 0914.65038 Erlingsson, Úlfar; Kaltofen, Erich; Musser, David 2 1996 Sparse multivariate function recovery with a high error rate in the evaluations. Zbl 1325.68289 Kaltofen, Erich L.; Yang, Zhengfeng 2 2014 Sparse multivariate function recovery from values with noise and outlier errors. Zbl 1360.94439 Kaltofen, Erich L.; Yang, Zhengfeng 2 2013 Supersparse black box rational function interpolation. Zbl 1323.68606 Kaltofen, Erich L.; Nehring, Michael 2 2011 Hermite rational function interpolation with error correction. Zbl 07635838 Kaltofen, Erich L.; Pernet, Clément; Yang, Zhi-Hong 2 2020 Computing approximate greatest common right divisors of differential polynomials. Zbl 1522.13037 Giesbrecht, Mark; Haraldson, Joseph; Kaltofen, Erich 2 2020 Analysis of the binary complexity of asymptotically fast algorithms for linear system solving. Zbl 0658.65027 Gregory, Brent; Kaltofen, Erich 1 1988 Symmetric determinantal representation of weakly-skew circuits. Zbl 1230.68221 Grenet, Bruno; Kaltofen, Erich L.; Koiran, Pascal; Portier, Natacha 1 2011 On the Berlekamp/Massey algorithm and counting singular Hankel matrices over a finite field. Zbl 1242.65074 Comer, Matthew T.; Kaltofen, Erich L. 1 2012 DSC – A system for distributed symbolic computation. Zbl 0925.68235 Diaz, A.; Kaltofen, E.; Schmitz, K.; Valente, T. 1 1991 Effective Hilbert irreducibility. Zbl 0584.12020 Kaltofen, Erich 1 1984 Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems. Zbl 0801.65024 Kaltofen, Erich 1 1993 Sparse polynomial interpolation codes and their decoding beyond half the minimum distance. Zbl 1325.68288 Kaltofen, Erich L.; Pernet, Clément 1 2014 Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of Seidenberg’s method. Zbl 1321.65077 Hutton, Sharon; Kaltofen, Erich L.; Zhi, Lihong 1 2010 Sparse multivariate function recovery with a small number of evaluations. Zbl 1338.94017 Kaltofen, Erich L.; Yang, Zhengfeng 1 2016 Numerical sparsity determination and early termination. Zbl 1365.65029 Hao, Zhiwei; Kaltofen, Erich L.; Zhi, Lihong 1 2016 Hermite rational function interpolation with error correction. Zbl 07635838 Kaltofen, Erich L.; Pernet, Clément; Yang, Zhi-Hong 2 2020 Computing approximate greatest common right divisors of differential polynomials. Zbl 1522.13037 Giesbrecht, Mark; Haraldson, Joseph; Kaltofen, Erich 2 2020 Sparse polynomial interpolation with arbitrary orthogonal polynomial bases. Zbl 1467.41002 Imamoglu, Erdal; Kaltofen, Erich L.; Yang, Zhengfeng 4 2018 Polynomial time interactive proofs for linear algebra with exponential matrix dimensions and scalars given by polynomial time circuits. Zbl 1457.68111 Dumas, Jean-Guillaume; Kaltofen, Erich L.; Villard, Gilles; Zhi, Lihong 1 2017 Early termination in parametric linear system solving and rational function vector recovery with error correction. Zbl 1462.65036 Kaltofen, Erich L.; Pernet, Clément; Storjohann, Arne; Waddell, Cleveland 1 2017 Linear time interactive certificates for the minimal polynomial and the determinant of a sparse matrix. Zbl 1365.65138 Dumas, Jean-Guillaume; Kaltofen, Erich; Thomé, Emmanuel; Villard, Gilles 4 2016 Sparse multivariate function recovery with a small number of evaluations. Zbl 1338.94017 Kaltofen, Erich L.; Yang, Zhengfeng 1 2016 Numerical sparsity determination and early termination. Zbl 1365.65029 Hao, Zhiwei; Kaltofen, Erich L.; Zhi, Lihong 1 2016 Error-correcting sparse interpolation in the Chebyshev basis. Zbl 1345.65004 Arnold, Andrew; Kaltofen, Erich L. 4 2015 Essentially optimal interactive certificates in linear algebra. Zbl 1325.68274 Dumas, Jean-Guillaume; Kaltofen, Erich 4 2014 Sparse multivariate function recovery with a high error rate in the evaluations. Zbl 1325.68289 Kaltofen, Erich L.; Yang, Zhengfeng 2 2014 Sparse polynomial interpolation codes and their decoding beyond half the minimum distance. Zbl 1325.68288 Kaltofen, Erich L.; Pernet, Clément 1 2014 Cleaning-up data for sparse model synthesis: when symbolic-numeric computation meets error-correcting codes. Zbl 1345.68287 Kaltofen, Erich L. 1 2014 Numerical linear system solving with parametric entries by error correction. Zbl 1345.65018 Boyer, Brice; Kaltofen, Erich L. 1 2014 Handbook of finite fields. Zbl 1319.11001 196 2013 On the matrix Berlekamp-Massey algorithm. Zbl 1301.65030 Kaltofen, Erich; Yuhasz, George 7 2013 A fraction free matrix Berlekamp/Massey algorithm. Zbl 1380.16050 Kaltofen, Erich; Yuhasz, George 3 2013 Sparse multivariate function recovery from values with noise and outlier errors. Zbl 1360.94439 Kaltofen, Erich L.; Yang, Zhengfeng 2 2013 Exact certification in global polynomial optimization via sums-of-squares of rational functions with rational coefficients. Zbl 1229.90115 Kaltofen, Erich L.; Li, Bin; Yang, Zhengfeng; Zhi, Lihong 27 2012 Sparse polynomial interpolation and Berlekamp/Massey algorithms that correct outlier errors in input values. Zbl 1323.65008 Comer, Matthew T.; Kaltofen, Erich L.; Pernet, Clément 4 2012 Certificates of impossibility of Hilbert-Artin representations of a given degree for definite polynomials and functions. Zbl 1323.65068 Guo, Feng; Kaltofen, Erich L.; Zhi, Lihong 3 2012 On the Berlekamp/Massey algorithm and counting singular Hankel matrices over a finite field. Zbl 1242.65074 Comer, Matthew T.; Kaltofen, Erich L. 1 2012 Symmetric determinantal representation of formulas and weakly skew circuits. Zbl 1261.68070 Grenet, Bruno; Kaltofen, Erich L.; Koiran, Pascal; Portier, Natacha 6 2011 Quadratic-time certificates in linear algebra. Zbl 1323.68607 Kaltofen, Erich L.; Nehring, Michael; Saunders, B. David 5 2011 Fast estimates of Hankel matrix condition numbers and numeric sparse interpolation. Zbl 1347.65037 Kaltofen, Erich L.; Lee, Wen-shin; Yang, Zhengfeng 4 2011 Supersparse black box rational function interpolation. Zbl 1323.68606 Kaltofen, Erich L.; Nehring, Michael 2 2011 Symmetric determinantal representation of weakly-skew circuits. Zbl 1230.68221 Grenet, Bruno; Kaltofen, Erich L.; Koiran, Pascal; Portier, Natacha 1 2011 Computing the radius of positive semidefiniteness of a multivariate real polynomial via a dual of Seidenberg’s method. Zbl 1321.65077 Hutton, Sharon; Kaltofen, Erich L.; Zhi, Lihong 1 2010 A proof of the monotone column permanent (MCP) conjecture for dimension 4 via sums-of-squares of rational functions. Zbl 1356.15002 Kaltofen, Erich; Yang, Zhengfeng; Zhi, Lihong 4 2009 Approximate factorization of multivariate polynomials using singular value decomposition. Zbl 1135.12003 Kaltofen, Erich; May, John P.; Yang, Zhengfeng; Zhi, Lihong 22 2008 Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars. Zbl 1493.68402 Kaltofen, Erich; Li, Bin; Yang, Zhengfeng; Zhi, Lihong 16 2008 Expressing a fraction of two determinants as a determinant. Zbl 1487.68255 Kaltofen, Erich; Koiran, Pascal 10 2008 Structures low rank approximation of a Sylvester matrix. Zbl 1117.65060 Kaltofen, Erich; Yang, Zhengfeng; Zhi, Lihong 24 2007 On exact and approximate interpolation of sparse rational functions. Zbl 1190.65019 Kaltofen, Erich; Yang, Zhengfeng 8 2007 Irreducible polynomials and Barker sequences. Zbl 1322.68271 Borwein, Peter; Kaltofen, Erich; Mossinghoff, Michael J. 3 2007 Approximate greatest common divisors of several polynomials with linearly constrained coefficients and singular polynomials. Zbl 1356.12011 Kaltofen, Erich; Yang, Zhengfeng; Zhi, Lihong 35 2006 Finding small degree factors of multivariate supersparse (lacunary) polynomials over algebraic number fields. Zbl 1356.11093 Kaltofen, Erich; Koiran, Pascal 10 2006 On the complexity of factoring bivariate supersparse (lacunary) polynomials. Zbl 1356.11092 Kaltofen, Erich; Koiran, Pascal 12 2005 Deterministic distinct-degree factorization of polynomials over finite fields. Zbl 1130.11336 Gao, Shuhong; Kaltofen, Erich; Lauder, Alan G. B. 3 2005 On the complexity of computing determinants. Zbl 1061.68185 Kaltofen, Erich; Villard, Gilles 34 2004 Approximate factorization of multivariate polynomials via differential equations. Zbl 1134.65346 Gao, Shuhong; Kaltofen, Erich; May, John; Yang, Zhengfeng; Zhi, Lihong 16 2004 Computing the sign or the value of the determinant of an integer matrix, a complexity survey. Zbl 1037.65044 Kaltofen, Erich; Villard, Gilles 7 2004 Early termination in sparse interpolation algorithms. Zbl 1074.68080 Kaltofen, Erich; Lee, Wen-shin 30 2003 Computer algebra handbook. Foundations, applications, systems. With CD-ROM, demo versions. Zbl 1017.68162 18 2003 Polynomial factorization: a success story. Zbl 1068.68709 Kaltofen, Erich 17 2003 On approximate irreducibility of polynomials in several variables. Zbl 1072.68676 Kaltofen, Erich; May, John 8 2003 Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases. Zbl 1074.68078 Giesbrecht, Mark; Kaltofen, Erich; Lee, Wen-shin 4 2003 Efficient matrix preconditioners for black box linear algebra. Zbl 0997.65073 Chen, Li; Eberly, Wayne; Kaltofen, Erich; Saunders, B. David; Turner, William J.; Villard, Gilles 9 2002 LinBox: A generic library for exact linear algebra. Zbl 1011.68182 Dumas, J.-G.; Gautier, T.; Giesbrecht, M.; Giorgi, P.; Hovinen, B.; Kaltofen, E.; Saunders, B. D.; Turner, W. J.; Villard, G. 8 2002 Algorithms for computing the sparsest shifts of polynomials via the Berlekamp/Massey algorithm. Zbl 1072.68669 Giesbrecht, Mark; Kaltofen, Erich; Lee, Wen-shin 3 2002 An output-sensitive variant of the baby steps/giant steps determinant algorithm. Zbl 1072.68675 Kaltofen, Erich 3 2002 On the complexity of computing determinants. (Extended abstract). Zbl 1012.65505 Kaltofen, Erich; Villard, Gilles 7 2001 Challenges of symbolic computation: My favorite open problems. With an additional open problem by Robert M. Corless and David J. Jeffrey. Zbl 0963.68234 Kaltofen, Erich 16 2000 Early termination in Ben-Or/Tiwari sparse interpolation and a hybrid of Zippel’s algorithm. Zbl 1326.68358 Kaltofen, Erich; Lee, Wen-shin; Lobo, Austin A. 14 2000 Distributed matrix-free solution of large sparse linear systems over finite fields. Zbl 1078.65542 Kaltofen, E.; Lobo, A. 6 1999 Subquadratic-time factoring of polynomials over finite fields. Zbl 0902.11053 Kaltofen, Erich; Shoup, Victor 46 1998 Efficient algorithms for computing the nearest polynomial with constrained roots. Zbl 0917.65045 Hitz, Markus A.; Kaltofen, Erich 17 1998 FOXBOX: A system for manipulating symbolic objects in black box representation. Zbl 0918.68049 Díaz, Angel; Kaltofen, Erich 8 1998 Fast polynomial factorization over high algebraic extensions of finite fields. Zbl 0920.11082 Kaltofen, Erich; Shoup, Victor 13 1997 On randomized Lanczos algorithms. Zbl 0917.65025 Eberly, Wayne; Kaltofen, Erich 10 1997 Second international symposium on parallel symbolic computation, PASCO ’97, Maui, HI, USA, July 20–22, 1997. Zbl 0903.00086 2 1997 On rank properties of Toeplitz matrices over finite fields. Zbl 0914.65039 Kaltofen, E.; Lobo, A. 13 1996 Generic Gram-Schmidt orthogonalization by exact division. Zbl 0914.65038 Erlingsson, Úlfar; Kaltofen, Erich; Musser, David 2 1996 Effective Noether irreducibility forms and applications. Zbl 0844.12006 Kaltofen, Erich 27 1995 Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems. Zbl 0828.65035 Kaltofen, Erich 19 1995 Integer division in residue number systems. Zbl 1053.68501 Hitz, Markus A.; Kaltofen, Erich 6 1995 On computing greatest common divisors with polynomials given by black boxes for their evaluations. Zbl 0919.12007 Díaz, Angel; Kaltofen, Erich 5 1995 Subquadratic-time factoring of polynomials over finite fields. Zbl 0921.11068 Kaltofen, Erich; Shoup, Victor 4 1995 Asymptotically fast solution of Toeplitz-like singular linear systems. Zbl 0978.15500 Kaltofen, Erich 8 1994 Factoring high-degree polynomials by the black box Berlekamp algorithm. Zbl 0978.68792 Kaltofen, Erich; Lobo, Austin 7 1994 Analysis of Coppersmith’s block Wiedemann algorithm for the parallel solution of sparse linear systems. Zbl 0801.65024 Kaltofen, Erich 1 1993 On computing determinants of matrices without divisions. Zbl 0978.65502 Kaltofen, Erich 13 1992 Processor-efficient parallel solution of linear systems. II: The positive characteristic and singular cases. (Extended abstract). Zbl 0977.68879 Kaltofen, Erich; Pan, Victor 9 1992 On fast multiplication of polynomials over arbitrary algebras. Zbl 0766.68055 Cantor, David G.; Kaltofen, Erich 114 1991 On Wiedemann’s method of solving sparse linear systems. Zbl 0778.65034 Kaltofen, Erich; Saunders, B. David 28 1991 Explicit construction of the Hilbert class fields of imaginary quadratic fields by integer lattice reduction. Zbl 0737.11034 Kaltofen, Erich; Yui, Noriko 5 1991 DSC – A system for distributed symbolic computation. Zbl 0925.68235 Diaz, A.; Kaltofen, E.; Schmitz, K.; Valente, T. 1 1991 Computing with polynomials given by black boxes for their evaluations: greatest common divisors, factorization, separation of numerators and denominators. Zbl 0712.12001 Kaltofen, Erich; Trager, Barry M. 39 1990 Polynomial factorization 1982-1986. Zbl 0773.11078 Kaltofen, Erich 16 1990 Parallel algorithms for matrix normal forms. Zbl 0727.65031 Kaltofen, Erich; Krishnamoorthy, M. S. 14 1990 Computing the irreducible real factors and components of an algebraic curve. Zbl 0737.14018 Kaltofen, Erich 3 1990 Computing greatest common divisors and factorizations in quadratic number fields. Zbl 0687.12001 Kaltofen, Erich; Rolletschek, Heinrich 7 1989 Mr. Smith goes to Las Vegas: randomized parallel computation of the Smith normal form of polynomial matrices. Zbl 1209.15003 Kaltofen, Erich; Krishnamoorthy, M. S.; Saunders, B. David 5 1989 Greatest common divisors of polynomials given by straight-line programs. Zbl 0642.68058 Kaltofen, Erich 21 1988 Efficient parallel evaluation of straight-line code and arithmetic circuits. Zbl 0651.68044 Miller, Gary L.; Ramachandran, Vijaya; Kaltofen, Erich 11 1988 Dagwood: A system for manipulating polynomials given by straight-line programs. Zbl 0825.68435 Freeman, Timothy S.; Imirzian, Gregory M.; Kaltofen, Erich; Yagati, Lakshman 6 1988 Analysis of the binary complexity of asymptotically fast algorithms for linear system solving. Zbl 0658.65027 Gregory, Brent; Kaltofen, Erich 1 1988 Fast parallel computation of Hermite and Smith forms of polynomial matrices. Zbl 0655.65069 Kaltofen, Erich; Krishnamoorthy, M. S.; Saunders, B. David 17 1987 Deterministic irreducibility testing of polynomials over large finite fields. Zbl 0683.68037 Kaltofen, E. 7 1987 Efficient parallel evaluation of straight-line code and arithmetic circuits. Zbl 0595.68043 Miller, Gary L.; Ramachandran, Vijaya; Kaltofen, Erich 6 1986 Polynomial-time reductions from multivariate to bi- and univariate integral polynomial factorization. Zbl 0605.12001 Kaltofen, Erich 45 1985 Fast parallel absolute irreducibility testing. Zbl 0599.68038 Kaltofen, Erich 29 1985 Factoring sparse multivariate polynomials. Zbl 0599.68037 von zur Gathen, Joachim; Kaltofen, Erich 25 1985 Factorization of multivariate polynomials over finite fields. Zbl 0596.12017 von zur Gathen, Joachim; Kaltofen, Erich 20 1985 Sparse Hensel lifting. Zbl 0605.12011 Kaltofen, Erich 17 1985 Effective Hilbert irreducibility. Zbl 0584.12019 Kaltofen, Erich 9 1985 Arithmetic in quadratic fields with unique factorization. Zbl 0596.12001 Kaltofen, Erich; Rolletschek, Heinrich 3 1985 Explicit construction of the Hilbert class fields of imaginary quadratic fields with class numbers 7 and 11. Zbl 0583.12007 Kaltofen, Erich; Yui, Noriko 5 1984 A note on the Risch differential equation. Zbl 0583.68015 Kaltofen, Erich 3 1984 Effective Hilbert irreducibility. Zbl 0584.12020 Kaltofen, Erich 1 1984 ...and 4 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 918 Authors 28 Schost, Éric 24 Kaltofen, Erich L. 23 van der Hoeven, Joris 20 Lecerf, Grégoire 15 von zur Gathen, Joachim 14 Pan, Victor Yakovlevich 13 Giesbrecht, Mark W. 11 Bostan, Alin 11 Lee, Wen-shin 11 Villard, Gilles 9 Chèze, Guillaume 9 Labahn, George 9 Winkler, Joab R. 8 Cuyt, Annie A. M. 8 Gao, Shuhong 8 Storjohann, Arne 7 Berthomieu, Jérémy 7 Emiris, Ioannis Z. 7 Neiger, Vincent 7 Saunders, B. David 7 Yang, Zhengfeng 6 Dumas, Jean-Guillaume 6 Faugère, Jean-Charles 6 Galligo, André 6 Jeannerod, Claude-Pierre 6 Koiran, Pascal 6 Monagan, Michael B. 6 Safey El Din, Mohab 6 Sekigawa, Hiroshi 6 Zhi, Lihong 5 Gashkov, Sergey B. 5 Grenet, Bruno 5 Huang, Qiaolong 5 Ivanyos, Gábor 5 Nagasaka, Kosaku 5 Pernet, Clément 5 Poteaux, Adrien 5 Rojas, J. Maurice 5 Sasaki, Tateaki 5 Saxena, Nitin 5 Sergeev, Igor’ Sergeevich 5 Shoup, Victor 4 Bourne, Martin 4 Doliskani, Javad 4 Feng, Yong 4 Gaudry, Pierrick 4 Harvey, David 4 Hu, Wenyu 4 Karpinski, Marek 4 Magron, Victor 4 Mahajan, Meena 4 Matera, Guillermo 4 Mitrouli, Marilena 4 Moreno-Centeno, Erick 4 Panario, Daniel 4 Roche, Daniel S. 4 Salvy, Bruno 4 Su, Yi 4 Szántó, Ágnes 4 Tsigaridas, Elias P. 4 Weimann, Martin 4 Wu, Min 4 Zeng, Zhenbing 3 Abu Salem, Fatima K. 3 Avendano, Martin 3 Batselier, Kim 3 Chen, Jingwei 3 Coxon, Nicholas 3 Dahan, Xavier 3 De Feo, Luca 3 De Moor, Bart L. 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