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Article: Circulant preconditioners for indefinite toeplitz systems
Title | Circulant preconditioners for indefinite toeplitz systems |
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Authors | |
Keywords | Circulant matrices Banded matrices Preconditioned conjugate-gradient-type method Indefinite toeplitz systems |
Issue Date | 2001 |
Citation | BIT Numerical Mathematics, 2001, v. 41, n. 5, p. 1079-1088 How to Cite? |
Abstract | In recent papers circulant preconditioners were proposed for ill-conditioned Hermitian Toeplitz matrices generated by 2π-periodic continuous functions with zeros of even order. It was shown that the spectra of the preconditioned matrices are uniformly bounded except for a finite number of outliers and therefore the conjugate gradient method, when applied to solving these circulant preconditioned systems, converges very quickly. In this paper, we consider indefinite Toeplitz matrices generated by 2π-periodic continuous functions with zeros of odd order. In particular, we show that the singular values of the preconditioned matrices are essentially bounded. Numerical results are presented to illustrate the fast convergence of CGNE, MINRES and QMR methods. © Swets & Zeitlinger. |
Persistent Identifier | http://hdl.handle.net/10722/276783 |
ISSN | 2023 Impact Factor: 1.6 2023 SCImago Journal Rankings: 1.064 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Ng, Michael K. | - |
dc.contributor.author | Potts, Daniel | - |
dc.date.accessioned | 2019-09-18T08:34:39Z | - |
dc.date.available | 2019-09-18T08:34:39Z | - |
dc.date.issued | 2001 | - |
dc.identifier.citation | BIT Numerical Mathematics, 2001, v. 41, n. 5, p. 1079-1088 | - |
dc.identifier.issn | 0006-3835 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276783 | - |
dc.description.abstract | In recent papers circulant preconditioners were proposed for ill-conditioned Hermitian Toeplitz matrices generated by 2π-periodic continuous functions with zeros of even order. It was shown that the spectra of the preconditioned matrices are uniformly bounded except for a finite number of outliers and therefore the conjugate gradient method, when applied to solving these circulant preconditioned systems, converges very quickly. In this paper, we consider indefinite Toeplitz matrices generated by 2π-periodic continuous functions with zeros of odd order. In particular, we show that the singular values of the preconditioned matrices are essentially bounded. Numerical results are presented to illustrate the fast convergence of CGNE, MINRES and QMR methods. © Swets & Zeitlinger. | - |
dc.language | eng | - |
dc.relation.ispartof | BIT Numerical Mathematics | - |
dc.subject | Circulant matrices | - |
dc.subject | Banded matrices | - |
dc.subject | Preconditioned conjugate-gradient-type method | - |
dc.subject | Indefinite toeplitz systems | - |
dc.title | Circulant preconditioners for indefinite toeplitz systems | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1023/A:1021905715654 | - |
dc.identifier.scopus | eid_2-s2.0-27844590536 | - |
dc.identifier.volume | 41 | - |
dc.identifier.issue | 5 | - |
dc.identifier.spage | 1079 | - |
dc.identifier.epage | 1088 | - |
dc.identifier.isi | WOS:000173977700022 | - |
dc.identifier.issnl | 0006-3835 | - |