High Performance Implementation of Matrix-vector Multiplications in Large-scale Sparse Matrix Eigenvalue Computations on the SMP-type Parallel Computer(<Special Issue>Algorithms for Matrix・Eigenvalue Problems and their Applications)

Abstract

Large-scale sparse matrix computations perform unsatisfactory on the parallel computers. The aim of this paper is to present a high performance implementation of Lanczos eigensolver. A method of bandwidth reduction type ordering is applied for matrix-vector multiplications, one of the main parts in Lanczos eigensolvers. The results show that the implementation with the method performs about 1.6 times faster in the best case. This implies that the ordering, which is known as effective in linear solvers, is also effective in the eigensolver.