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

In this paper we present a master–worker type parallel method for finding several eigenvalues and eigenvectors of a generalized eigenvalue problem Ax=λBx, where AA and BB 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 AA and BB. 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.