A parallel method for large sparse generalized Eigenvalue problems by OmniRPC in a grid environment

Abstract

In this paper we present a parallel method for finding several eigen-values and eigenvectors of a generalized eigenvalue problem Ax = λBx, where A and B are large sparse matrices. A moment-based method by which to find all of the eigenvalues that lie inside a given domain is used. In this method, a small matrix pencil that has only the desired eigenvalues is derived by solving large sparse systems of linear equations constructed from A and B. Since these equations can be solved independently, we solve them on remote hosts in parallel. This approach is suitable for master-worker programming models. We have implemented and tested the proposed method in a grid environment using a grid RPC (remote procedure call) system called OmniRPC. The performance of the method on PC clusters that were used over a wide-area network was evaluated. © Springer-Verlag Berlin Heidelberg 2006.