Parallel Multicore CSB Format and Its Sparse Matrix Vector Multiplication

Abstract

Sparse Matrix Vector Multiplication (SpMV) is one of the most basic problems in scientific and engineering computations. It is the basic operation in many realms, such as solving linear systems or eigenvalue problems. Nowadays, more than 90 percent of the world’s highest performance parallel computers in the top 500 use multicore architecture. So it is important practically to design the efficient methods of computing SpMV on multicore parallel computers. Usually, algorithms based on compressed sparse row (CSR) format suffer from a number of nonzero elements on each row so hardly as to use the multicore structure efficiently. Compressed Sparse Block (CSB) format is an effective storage format which can compute SpMV efficiently in a multicore computer. This paper presents a parallel multicore CSB format and SpMV based on it. We carried out numerical experiments on a parallel multicore computer. The results show that our parallel multicore CSB format and SpMV algorithm can reach high speedup, and they are highly scalable for banded matrices.