Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
Exploiting fast matrix multiplication within the level 3 BLAS
ACM Transactions on Mathematical Software (TOMS)
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
GEMMW: a portable level 3 BLAS Winograd variant of Strassen's matrix-matrix multiply algorithm
Journal of Computational Physics
Matrix computations (3rd ed.)
Modern computer algebra
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Discrete Logarithms: The Past and the Future
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Implementation of Strassen's algorithm for matrix multiplication
Supercomputing '96 Proceedings of the 1996 ACM/IEEE conference on Supercomputing
On efficient sparse integer matrix Smith normal form computations
Journal of Symbolic Computation - Special issue on computer algebra and mechanized reasoning: selected St. Andrews' ISSAC/Calculemus 2000 contributions
Black box methods for least squares problems
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Recursive Blocked Data Formats and BLAS's for Dense Linear Algebra Algorithms
PARA '98 Proceedings of the 4th International Workshop on Applied Parallel Computing, Large Scale Scientific and Industrial Problems
On parallel block algorithms for exact triangularizations
Parallel Computing
Finite field linear algebra subroutines
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
On the complexity of polynomial matrix computations
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
FFPACK: finite field linear algebra package
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
The aggregation and cancellation techniques as a practical tool for faster matrix multiplication
Theoretical Computer Science - Algebraic and numerical algorithm
On the complexity of computing determinants
Computational Complexity
Efficient computation of the characteristic polynomial
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
The shifted number system for fast linear algebra on integer matrices
Journal of Complexity - Festschrift for the 70th birthday of Arnold Schönhage
A block Lanczos algorithm for finding dependencies over GF(2)
EUROCRYPT'95 Proceedings of the 14th annual international conference on Theory and application of cryptographic techniques
Self-adapting numerical software and automatic tuning of heuristics
ICCS'03 Proceedings of the 2003 international conference on Computational science
Self-adapting numerical software and automatic tuning of heuristics
ICCS'03 Proceedings of the 2003 international conference on Computational science
Generic design of Chinese remaindering schemes
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Exact sparse matrix-vector multiplication on GPU's and multicore architectures
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
Parallel Gaussian elimination for Gröbner bases computations in finite fields
Proceedings of the 4th International Workshop on Parallel and Symbolic Computation
LINBOX founding scope allocation, parallel building blocks, and separate compilation
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Solving Very Sparse Rational Systems of Equations
ACM Transactions on Mathematical Software (TOMS)
Exact solutions to linear systems of equations using output sensitive lifting
ACM Communications in Computer Algebra
Simultaneous computation of the row and column rank profiles
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
Fast matrix decomposition in F2
Journal of Computational and Applied Mathematics
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In the past two decades, some major efforts have been made to reduce exact (e.g. integer, rational, polynomial) linear algebra problems to matrix multiplication in order to provide algorithms with optimal asymptotic complexity. To provide efficient implementations of such algorithms one need to be careful with the underlying arithmetic. It is well known that modular techniques such as the Chinese remainder algorithm or the p-adic lifting allow very good practical performance, especially when word size arithmetic is used. Therefore, finite field arithmetic becomes an important core for efficient exact linear algebra libraries. In this article, we study high performance implementations of basic linear algebra routines over word size prime fields: especially matrix multiplication; our goal being to provide an exact alternate to the numerical BLAS library. We show that this is made possible by a careful combination of numerical computations and asymptotically faster algorithms. Our kernel has several symbolic linear algebra applications enabled by diverse matrix multiplication reductions: symbolic triangularization, system solving, determinant, and matrix inverse implementations are thus studied.