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)
An introduction to parallel algorithms
An introduction to parallel algorithms
Introduction to parallel computing: design and analysis of algorithms
Introduction to parallel computing: design and analysis of algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
Polynomial and matrix computations (vol. 1): fundamental algorithms
SIAM Journal on Discrete Mathematics
Minimal Resolutions and the Homology of Matching and Chessboard Complexes
Journal of Algebraic Combinatorics: An International Journal
Integer Smith form via the valence: experience with large sparse matrices from homology
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
A parallel block algorithm for exact triangularization of rectangular matrices
Proceedings of the thirteenth annual ACM symposium on Parallel algorithms and architectures
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Finite field linear algebra subroutines
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Athapascan-1: On-Line Building Data Flow Graph in a Parallel Language
PACT '98 Proceedings of the 1998 International Conference on Parallel Architectures and Compilation Techniques
FFPACK: finite field linear algebra package
ISSAC '04 Proceedings of the 2004 international symposium on Symbolic and algebraic computation
Dense Linear Algebra over Word-Size Prime Fields: the FFLAS and FFPACK Packages
ACM Transactions on Mathematical Software (TOMS)
Simultaneous computation of the row and column rank profiles
Proceedings of the 38th international symposium on International symposium on symbolic and algebraic computation
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We present a new parallel algorithm to compute an exact triangularization of large square or rectangular and dense or sparse matrices in any field. Using fast matrix multiplication, our algorithm has the best known sequential arithmetic complexity. Furthermore, on distributed architectures, it drastically reduces the total volume of communication compared to previously known algorithms. The resulting matrix can be used to compute the rank or to solve a linear system. Over finite fields, for instance, our method has proven useful in the computation of large Gröbner bases arising in robotic problems or wavelet image compression.