A Moment‐Based Method for Large‐Scale Generalized Eigenvalue Problems
Tetsuya Sakurai, Hiroto Tadano, Yuichi Inadomi⋆, Umpei Nagashima · Applied Numerical Analysis & Computational Mathematics · 2004
Abstract In this paper we consider a method for finding several eigenvalues and corresponding eigenvectors of large‐scale generalized eigenvalue problems. In this method, a small matrix pencil that has only the desired eigenvalues is derived using complex moments obtained via numerical integration. Since the process to derive the moments can be performed in parallel and we do not need to exchange data between processes, the presented method is suitable for master‐worker programming models. We have implemented and tested the proposed method in a grid RPC (remote procedure call) system. Numerical examples illustrate the properties of our approach. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)