Performance Improvement of Sparse Matrix Vector Product on Vector Machines

Abstract

Abstract. Many applications based on finite element and finite difference methods include the solution of large sparse linear systems using preconditioned iterative methods. Matrix vector multiplication is one of the key operations that has a significant impact on the performance of any iterative solver. In this paper, recent developments in sparse storage formats on vector machines are reviewed. Then, several improvements to memory access in the sparse matrix vector product are suggested. Particularly, algorithms based on dense blocks are discussed and reasons for their superior performance are explained. Finally, the performance gain by the presented modifications is demonstrated.

Block-Based Approach to Solving Linear Systems

“…Using vector registers to reduce memory operations for loading and storing the result vector further improves the performance of JAD based sparse MVP to 2.2 GFlop/s. Further optimizations result in a maximum performance of 20% vector peak (which is 16 GFlop/s) for sparse MVP on NEC SX-8 [6].…”

“…Thus, small blocks can be formed by grouping the equations at each grid point. Operating on such dense blocks considerably reduces the amount of indirect addressing required for sparse MVP [6]. This improves the performance of the kernel dramatically on vector machines [9] and also remarkably on superscalar architectures [10,11].…”