Abstract
In this paper we present a parallel method for finding several eigenvalues and eigenvectors of a generalized eigenvalue problem A x = λB x, 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.
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Sakurai, T., Hayakawa, K., Sato, M., Takahashi, D. (2006). A Parallel Method for Large Sparse Generalized Eigenvalue Problems by OmniRPC in a Grid Environment. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_138
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DOI: https://doi.org/10.1007/11558958_138
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29067-4
Online ISBN: 978-3-540-33498-9
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