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

Authors:
Tetsuya Sakurai;Kentaro Hayakawa;Mitsuhisa Sato;Daisuke Takahashi
Affiliations:
,Department of Computer Science, University of Tsukuba, Tsukuba, Japan;Doctoral Program of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan;Department of Computer Science, University of Tsukuba, Tsukuba, Japan;Department of Computer Science, University of Tsukuba, Tsukuba, Japan
Venue:
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
Year:
2004

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Abstract

In this paper we present a parallel method for finding several eigenvalues 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.