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

TL;DR

This paper presents optimized implementations of sparse matrix-vector multiplication on GPUs and multicore CPUs to enhance the performance of algebraic algorithms over finite fields, leveraging parallelization techniques.

Contribution

It introduces new GPU and multicore implementations of sparse matrix-vector multiplication and applies them to improve finite field algebraic algorithms within the LinBox library.

Findings

Significant speedup of sparse matrix-vector multiplication on GPU and multicore architectures.

Enhanced performance of black box algorithms over finite fields.

Parallelization of the sigma-basis algorithm in a block Wiedemann rank implementation.

Abstract

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.