A filter diagonalization for generalized eigenvalue problems based on the Sakurai-Sugiura projection method

Authors:
Tsutomu Ikegami;Tetsuya Sakurai;Umpei Nagashima
Affiliations:
Information Technology Research Institute, AIST, 1-1-1 Umezono, Tsukuba 305-8568, Japan;Department of Computer Science, University of Tsukuba, Tsukuba 305-8573, Japan;Research Institute for Computational Science, AIST, 1-1-1 Umezono, Tsukuba 305-8568, Japan
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

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Abstract

The Sakurai-Sugiura projection method, which solves generalized eigenvalue problems to find certain eigenvalues in a given domain, was reformulated by using the resolvent theory. A new interpretation based on filter diagonalization was given, and the corresponding filter function was derived explicitly. A block version of the method was also proposed, which enabled not only resolution of degenerated eigenvalues, but also an improvement in numerical accuracy. Three numerical examples were provided to illustrate the method.