Volume 1, Issue 3
A Multilevel Spectral Indicator Method for Eigenvalues of Large Non-Hermitian Matrices

CSIAM Trans. Appl. Math., 1 (2020), pp. 463-477.

Published online: 2020-09

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• 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.

• Keywords

Eigenvalue problems, spectral indicator method, non-Hermitian matrix.

65F15, 47A10, 65F10

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@Article{CSIAM-AM-1-463, author = {Ruihao Huang , and Jiguang Sun , and Chao Yang , }, title = {A Multilevel Spectral Indicator Method for Eigenvalues of Large Non-Hermitian Matrices}, journal = {CSIAM Transactions on Applied Mathematics}, year = {2020}, volume = {1}, number = {3}, pages = {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.

}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.2020-0021}, url = {http://global-sci.org/intro/article_detail/csiam-am/18303.html} }
TY - JOUR T1 - A Multilevel Spectral Indicator Method for Eigenvalues of Large Non-Hermitian Matrices AU - Ruihao Huang , AU - Jiguang Sun , AU - Chao Yang , JO - CSIAM Transactions on Applied Mathematics VL - 3 SP - 463 EP - 477 PY - 2020 DA - 2020/09 SN - 1 DO - http://doi.org/10.4208/csiam-am.2020-0021 UR - https://global-sci.org/intro/article_detail/csiam-am/18303.html KW - Eigenvalue problems, spectral indicator method, non-Hermitian matrix. AB -

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.

Ruihao Huang, Jiguang Sun & Chao Yang. (2020). A Multilevel Spectral Indicator Method for Eigenvalues of Large Non-Hermitian Matrices. CSIAM Transactions on Applied Mathematics. 1 (3). 463-477. doi:10.4208/csiam-am.2020-0021
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