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We propose different implementations of the sparse matrix--dense vectormultiplication (\spmv{}) for finite fields and rings $\Zb/m\Zb$. We takeadvantage of graphic card processors (GPU) and multi-core architectures. Ouraim is to improve the speed of \spmv{} in the \linbox library, and henceforththe speed of its black box algorithms. Besides, we use this and a newparallelization of the sigma-basis algorithm in a parallel block Wiedemann rankimplementation over finite fields.

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