Title of Paper:Relationships among contour integral-based methods for solving generalized eigenvalue problems

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Date of Publication:2016-12-01

Journal:JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS

Included Journals:SCIE、EI、Scopus

Volume:33

Issue:3

Page Number:721-750

ISSN No.:0916-7005

Key Words:Generalized eigenvalue problems; Contour integral-based eigensolvers; Projection methods

Abstract:Recently, contour integral-based methods have been actively studied for solving interior eigenvalue problems that find all eigenvalues located in a certain region and their corresponding eigenvectors. In this paper, we reconsider the algorithms of the five typical contour integral-based eigensolvers from the viewpoint of projection methods, and then map the relationships among these methods. From the analysis, we conclude that all contour integral-based eigensolvers can be regarded as projection methods and can be categorized based on their subspace used, the type of projection and the problem to which they are applied implicitly.