A parallel method for large sparse generalized eigenvalue problems using a GridRPC system

  • Authors:

  • Tetsuya Sakurai;Yoshihisa Kodaki;Hiroto Tadano;Daisuke Takahashi;Mitsuhisa Sato;Umpei Nagashima

  • Affiliations:

  • Department of Computer Science, University of Tsukuba, Tsukuba 305-8573, Japan;Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba 305-8573, Japan;Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan;Department of Computer Science, University of Tsukuba, Tsukuba 305-8573, Japan;Department of Computer Science, University of Tsukuba, Tsukuba 305-8573, Japan;Research Institute of Computational Science, AIST, Tsukuba 305-8568, Japan

  • Venue:
  • Future Generation Computer Systems
  • Year:
  • 2008

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Abstract

In this paper we present a master-worker type parallel method for finding several eigenvalues and eigenvectors of a generalized eigenvalue problem Ax=@lBx, where A and B are large sparse matrices. A moment-based method that finds 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 servers 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.