Exact Sparse Matrix-Vector Multiplication on GPU's and Multicore Architectures

We propose different implementations of the sparse matrix--dense vector multiplication (\spmv{}) for finite fields and rings \Zb/m\Zb. We take advantage of graphic card processors (GPU) and multi-core architectures. Our aim is to improve the speed of \spmv{} in the \linbox library, and henceforth the speed of its black box algorithms. Besides, we use this and a new parallelization of the sigma-basis algorithm in a parallel block Wiedemann rank implementation over finite fields

Computational linear algebra over finite fields

We present here algorithms for efficient computation of linear algebra problems over finite fields

Compressed Modular Matrix Multiplication

We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly accessible but modular dot product can be performed by an integer multiplication by the reverse integer. Modular multiplication by a word containing a single residue is a also possible. Therefore matrix multiplication can be performed on such a compressed storage. We here give bounds on the sizes of primes and matrices for which such a compression is possible. We also explicit the details of the required compressed arithmetic routines.Comment: Published in: MICA'2008 : Milestones in Computer Algebra, Tobago : Trinit\'e-et-Tobago (2008