Year: 2020
Author: Ruihao Huang, Jiguang Sun, Chao Yang
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 3 : pp. 463–477
Abstract
Recently a novel family of eigensolvers, called spectral indicator methods (SIMs), was proposed. Given a region on the complex plane, SIMs first compute an indicator by the spectral projection. The indicator is used to test if the region contains eigenvalue(s). Then the region containing eigenvalues(s) is subdivided and tested. The procedure is repeated until the eigenvalues are identified within a specified precision. In this paper, using Cayley transformation and Krylov subspaces, a memory efficient multilevel eigensolver is proposed. The method uses less memory compared with the early versions of SIMs and is particularly suitable to compute many eigenvalues of large sparse (non-Hermitian) matrices. Several examples are presented for demonstration.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/csiam-am.2020-0021
CSIAM Transactions on Applied Mathematics, Vol. 1 (2020), Iss. 3 : pp. 463–477
Published online: 2020-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Eigenvalue problems spectral indicator method non-Hermitian matrix.