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Conference Paper: On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations
Title | On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations |
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Authors | |
Keywords | Normal matrix Skew-Hermitian matrix Splitting iteration method Successive overrelaxation Hermitian matrix Non-hermitian matrix |
Issue Date | 2007 |
Citation | Numerical Linear Algebra with Applications, 2007, v. 14, n. 4, p. 319-335 How to Cite? |
Abstract | We further generalize the technique for constructing the Hermitian/skew-Hermitian splitting (HSS) iteration method for solving large sparse non-Hermitian positive definite system of linear equations to the normal/skew-Hermitian (NS) splitting obtaining a class of normal/skew-Hermitian splitting (NSS) iteration methods. Theoretical analyses show that the NSS method converges unconditionally to the exact solution of the system of linear equations. Moreover, we derive an upper bound of the contraction factor of the NSS iteration which is dependent solely on the spectrum of the normal splitting matrix, and is independent of the eigenvectors of the matrices involved. We present a successive-overrelaxation (SOR) acceleration scheme for the NSS iteration, which specifically results in an acceleration scheme for the HSS iteration. Convergence conditions for this SOR scheme are derived under the assumption that the eigenvalues of the corresponding block Jacobi iteration matrix lie in certain regions in the complex plane. A numerical example is used to show that the SOR technique can significantly accelerate the convergence rate of the NSS or the HSS iteration method. Copyright © 2007 John Wiley & Sons, Ltd. |
Persistent Identifier | http://hdl.handle.net/10722/276806 |
ISSN | 2023 Impact Factor: 1.8 2023 SCImago Journal Rankings: 0.932 |
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 | 2019-09-18T08:34:43Z | - |
dc.date.available | 2019-09-18T08:34:43Z | - |
dc.date.issued | 2007 | - |
dc.identifier.citation | Numerical Linear Algebra with Applications, 2007, v. 14, n. 4, p. 319-335 | - |
dc.identifier.issn | 1070-5325 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276806 | - |
dc.description.abstract | We further generalize the technique for constructing the Hermitian/skew-Hermitian splitting (HSS) iteration method for solving large sparse non-Hermitian positive definite system of linear equations to the normal/skew-Hermitian (NS) splitting obtaining a class of normal/skew-Hermitian splitting (NSS) iteration methods. Theoretical analyses show that the NSS method converges unconditionally to the exact solution of the system of linear equations. Moreover, we derive an upper bound of the contraction factor of the NSS iteration which is dependent solely on the spectrum of the normal splitting matrix, and is independent of the eigenvectors of the matrices involved. We present a successive-overrelaxation (SOR) acceleration scheme for the NSS iteration, which specifically results in an acceleration scheme for the HSS iteration. Convergence conditions for this SOR scheme are derived under the assumption that the eigenvalues of the corresponding block Jacobi iteration matrix lie in certain regions in the complex plane. A numerical example is used to show that the SOR technique can significantly accelerate the convergence rate of the NSS or the HSS iteration method. Copyright © 2007 John Wiley & Sons, Ltd. | - |
dc.language | eng | - |
dc.relation.ispartof | Numerical Linear Algebra with Applications | - |
dc.subject | Normal matrix | - |
dc.subject | Skew-Hermitian matrix | - |
dc.subject | Splitting iteration method | - |
dc.subject | Successive overrelaxation | - |
dc.subject | Hermitian matrix | - |
dc.subject | Non-hermitian matrix | - |
dc.title | On successive-overrelaxation acceleration of the Hermitian and skew-Hermitian splitting iterations | - |
dc.type | Conference_Paper | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1002/nla.517 | - |
dc.identifier.scopus | eid_2-s2.0-34247490775 | - |
dc.identifier.volume | 14 | - |
dc.identifier.issue | 4 | - |
dc.identifier.spage | 319 | - |
dc.identifier.epage | 335 | - |
dc.identifier.isi | WOS:000245958400005 | - |
dc.identifier.issnl | 1070-5325 | - |