Solving sparse linear equations over finite fields
IEEE Transactions on Information Theory
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Exploiting fast matrix multiplication within the level 3 BLAS
ACM Transactions on Mathematical Software (TOMS)
Computation of discrete logarithms in prime fields
Designs, Codes and Cryptography
Solving homogeneous linear equations over GF(2) via block Wiedemann algorithm
Mathematics of Computation
GEMMW: a portable level 3 BLAS Winograd variant of Strassen's matrix-matrix multiply algorithm
Journal of Computational Physics
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
An approximate probabilistic model for structured Gaussian elimination
Journal of Algorithms
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Matrix analysis and applied linear algebra
Matrix analysis and applied linear algebra
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
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Recent Progress and Prospects for Integer Factorisation Algorithms
COCOON '00 Proceedings of the 6th Annual International Conference on Computing and Combinatorics
Solving Large Sparse Linear Systems over Finite Fields
CRYPTO '90 Proceedings of the 10th Annual International Cryptology Conference on Advances in Cryptology
Dense Linear Algebra over Word-Size Prime Fields: the FFLAS and FFPACK Packages
ACM Transactions on Mathematical Software (TOMS)
A Computational Introduction to Number Theory and Algebra
A Computational Introduction to Number Theory and Algebra
Algorithm 898: Efficient multiplication of dense matrices over GF(2)
ACM Transactions on Mathematical Software (TOMS)
NIST Handbook of Mathematical Functions
NIST Handbook of Mathematical Functions
| Hi-index | 7.29 |
In this work an efficient algorithm to perform a block decomposition for large dense rectangular matrices with entries in F"2 is presented. Matrices are stored as column blocks of row major matrices in order to facilitate rows operation and matrix multiplications with blocks of columns. One of the major bottlenecks of matrix decomposition is the pivoting involving both rows and column exchanges. Since row swaps are cheap and column swaps are order of magnitude slower, the number of column swaps should be reduced as much as possible. Here an algorithm that completely avoids the column permutations is presented. An asymptotically fast algorithm is obtained by combining the four Russian algorithm and the recursion with the Strassen algorithm for matrix-matrix multiplication. Moreover optimal parameters for the tuning of the algorithm are theoretically estimated and then experimentally verified. A comparison with the state of the art public domain software SAGE shows that the proposed algorithm is generally faster.