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Article: Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems
Title | Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems |
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Authors | |
Keywords | Non-Hermitian matrix Iterative methods Hermitian matrix Skew-Hermitian matrix Splitting |
Issue Date | 2003 |
Citation | SIAM Journal on Matrix Analysis and Applications, 2003, v. 24, n. 3, p. 603-626 How to Cite? |
Abstract | We study efficient iterative methods for the large sparse non-Hermitian positive definite system of linear equations based on the Hermitian and skew-Hermitian splitting of the coefficient matrix. These methods include a Hermitian/skew-Hermitian splitting (HSS) iteration and its inexact variant, the inexact Hermitian/skew-Hermitian splitting (IHSS) iteration, which employs some Krylov subspace methods as its inner iteration processes at each step of the outer HSS iteration. Theoretical analyses show that the HSS method converges unconditionally to the unique solution of the system of linear equations. Moreover, we derive an upper bound of the contraction factor of the HSS iteration which is dependent solely on the spectrum of the Hermitian part and is independent of the eigenvectors of the matrices involved. Numerical examples are presented to illustrate the effectiveness of both HSS and IHSS iterations. In addition, a model problem of a three-dimensional convection-diffusion equation is used to illustrate the advantages of our methods. |
Persistent Identifier | http://hdl.handle.net/10722/276739 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 1.042 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Bai, Zhong Zhi | - |
dc.contributor.author | Golub, Gene H. | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:30Z | - |
dc.date.available | 2019-09-18T08:34:30Z | - |
dc.date.issued | 2003 | - |
dc.identifier.citation | SIAM Journal on Matrix Analysis and Applications, 2003, v. 24, n. 3, p. 603-626 | - |
dc.identifier.issn | 0895-4798 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276739 | - |
dc.description.abstract | We study efficient iterative methods for the large sparse non-Hermitian positive definite system of linear equations based on the Hermitian and skew-Hermitian splitting of the coefficient matrix. These methods include a Hermitian/skew-Hermitian splitting (HSS) iteration and its inexact variant, the inexact Hermitian/skew-Hermitian splitting (IHSS) iteration, which employs some Krylov subspace methods as its inner iteration processes at each step of the outer HSS iteration. Theoretical analyses show that the HSS method converges unconditionally to the unique solution of the system of linear equations. Moreover, we derive an upper bound of the contraction factor of the HSS iteration which is dependent solely on the spectrum of the Hermitian part and is independent of the eigenvectors of the matrices involved. Numerical examples are presented to illustrate the effectiveness of both HSS and IHSS iterations. In addition, a model problem of a three-dimensional convection-diffusion equation is used to illustrate the advantages of our methods. | - |
dc.language | eng | - |
dc.relation.ispartof | SIAM Journal on Matrix Analysis and Applications | - |
dc.subject | Non-Hermitian matrix | - |
dc.subject | Iterative methods | - |
dc.subject | Hermitian matrix | - |
dc.subject | Skew-Hermitian matrix | - |
dc.subject | Splitting | - |
dc.title | Hermitian and skew-Hermitian splitting methods for non-Hermitian positive definite linear systems | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1137/S0895479801395458 | - |
dc.identifier.scopus | eid_2-s2.0-0042415257 | - |
dc.identifier.volume | 24 | - |
dc.identifier.issue | 3 | - |
dc.identifier.spage | 603 | - |
dc.identifier.epage | 626 | - |
dc.identifier.isi | WOS:000181153600001 | - |
dc.identifier.issnl | 0895-4798 | - |