A Comparison of Parallel Preconditioners for the Sparse generalized Eigenvalue Problems by Rayleigh-Quotient Minimization

Abstract

In this paper we address ourselves to the problem of finding efficient parallel preconditioner for the interior generalized eigenvalue problem Ax = λBx, where A and B are large sparse symmetric positive definite matrices. We consider incomplete LU(ILU)(0) in two variants, Multi-Color block successive over-relaxation(SOR), and Point-symmetric SOR(SSOR). Our results show that for small number of processors the Multi-Color ILU(0) gives the best performance, while for large number of processors the Multi-Color Block SOR does.