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Article: Factorized banded inverse preconditioners for matrices with Toeplitz structure
Title | Factorized banded inverse preconditioners for matrices with Toeplitz structure |
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Authors | |
Keywords | Inverse preconditioners Nonlinear image restoration Toeplitz-related matrices |
Issue Date | 2005 |
Publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/sisc.php |
Citation | SIAM Journal On Scientific Computing, 2005, v. 26 n. 6, p. 1852-1870 How to Cite? |
Abstract | In this paper, we study factorized banded inverse preconditioned for matrices with Toeplitz structure. We show that if a Toeplitz matrix T has certain off-diagonal decay property, then the factorized banded inverse preconditioner approximates T-1 accurately, and the spectra of these preconditioned matrices are clustered around 1. In nonlinear image restoration applications, Toeplitz-related systems of the form I+T* DT are required to solve, where D is a positive nonconstant diagonal matrix. We construct inverse preconditioners for such matrices. Numerical results show that the performance of our proposed preconditioners are superior to that of circulant preconditioners. A two-dimensional nonlinear image restoration example is also presented to demonstrate the effectiveness of the proposed preconditioner. © 2005 Society for Industrial and Applied Mathematics. |
Persistent Identifier | http://hdl.handle.net/10722/44908 |
ISSN | 2023 Impact Factor: 3.0 2023 SCImago Journal Rankings: 1.803 |
ISI Accession Number ID | |
References |
DC Field | Value | Language |
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dc.contributor.author | Lin, FR | en_HK |
dc.contributor.author | Ng, MK | en_HK |
dc.contributor.author | Ching, WK | en_HK |
dc.date.accessioned | 2007-10-30T06:13:10Z | - |
dc.date.available | 2007-10-30T06:13:10Z | - |
dc.date.issued | 2005 | en_HK |
dc.identifier.citation | SIAM Journal On Scientific Computing, 2005, v. 26 n. 6, p. 1852-1870 | en_HK |
dc.identifier.issn | 1064-8275 | en_HK |
dc.identifier.uri | http://hdl.handle.net/10722/44908 | - |
dc.description.abstract | In this paper, we study factorized banded inverse preconditioned for matrices with Toeplitz structure. We show that if a Toeplitz matrix T has certain off-diagonal decay property, then the factorized banded inverse preconditioner approximates T-1 accurately, and the spectra of these preconditioned matrices are clustered around 1. In nonlinear image restoration applications, Toeplitz-related systems of the form I+T* DT are required to solve, where D is a positive nonconstant diagonal matrix. We construct inverse preconditioners for such matrices. Numerical results show that the performance of our proposed preconditioners are superior to that of circulant preconditioners. A two-dimensional nonlinear image restoration example is also presented to demonstrate the effectiveness of the proposed preconditioner. © 2005 Society for Industrial and Applied Mathematics. | en_HK |
dc.format.extent | 818226 bytes | - |
dc.format.extent | 1815 bytes | - |
dc.format.mimetype | application/pdf | - |
dc.format.mimetype | text/plain | - |
dc.language | eng | en_HK |
dc.publisher | Society for Industrial and Applied Mathematics. The Journal's web site is located at http://www.siam.org/journals/sisc.php | - |
dc.relation.ispartof | SIAM Journal on Scientific Computing | en_HK |
dc.rights | © 2005 Society for Industrial and Applied Mathematics. First Published in SIAM Journal on Scientific Computing in volume 26, issue 6, published by the Society for Industrial and Applied Mathematics (SIAM). | - |
dc.subject | Inverse preconditioners | en_HK |
dc.subject | Nonlinear image restoration | en_HK |
dc.subject | Toeplitz-related matrices | en_HK |
dc.title | Factorized banded inverse preconditioners for matrices with Toeplitz structure | en_HK |
dc.type | Article | en_HK |
dc.identifier.openurl | http://library.hku.hk:4550/resserv?sid=HKU:IR&issn=1064-8275&volume=26&issue=6&spage=1852&epage=1870&date=2005&atitle=Factorized+banded+inverse+preconditioners+for+matrices+with+toeplitz+structure | en_HK |
dc.identifier.email | Ching, WK:wching@hku.hk | en_HK |
dc.identifier.authority | Ching, WK=rp00679 | en_HK |
dc.description.nature | published_or_final_version | en_HK |
dc.identifier.doi | 10.1137/030601272 | en_HK |
dc.identifier.scopus | eid_2-s2.0-27844585669 | en_HK |
dc.relation.references | http://www.scopus.com/mlt/select.url?eid=2-s2.0-27844585669&selection=ref&src=s&origin=recordpage | en_HK |
dc.identifier.volume | 26 | en_HK |
dc.identifier.issue | 6 | en_HK |
dc.identifier.spage | 1852 | en_HK |
dc.identifier.epage | 1870 | en_HK |
dc.identifier.isi | WOS:000231357700003 | - |
dc.publisher.place | United States | en_HK |
dc.identifier.scopusauthorid | Lin, FR=7402777425 | en_HK |
dc.identifier.scopusauthorid | Ng, MK=7202076432 | en_HK |
dc.identifier.scopusauthorid | Ching, WK=13310265500 | en_HK |
dc.identifier.issnl | 1064-8275 | - |