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- Publisher Website: 10.1016/S0024-3795(96)00295-9
- Scopus: eid_2-s2.0-0041154571
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Article: Band preconditioners for block-Toeplitz-Toeplitz-block systems
Title | Band preconditioners for block-Toeplitz-Toeplitz-block systems |
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Authors | |
Issue Date | 1997 |
Citation | Linear Algebra and Its Applications, 1997, v. 259, n. 1-3, p. 307-327 How to Cite? |
Abstract | Preconditioned conjugate gradient methods are employed to solve symmetric positive definite m-by-m block Toeplitz with n-by-n Toeplitz block systems Am, nx = b where Am, n are generated by 2π-Periodic nonnegative functions with zeros. Serra has proposed using band block Toeplitz with band Toeplitz block matrices Bm, n, with their external and internal bandwidths independent of m and n as preconditioners. Serra showed that if the Hessians of the generating function at the zeros are positive definite, then the condition number of B-1m, n Am, n is uniformly bounded by a constant independent of m and n, whereas the condition number of Am, n tends to infinity as m and n tend to infinity. In this paper, we provide a method for deriving band preconditioners for block-Toeplitz-Toeplitz-block matrices. Numerical examples are given to illustrate the performance of the method. © Elsevier Science Inc., 1997. |
Persistent Identifier | http://hdl.handle.net/10722/276735 |
ISSN | 2023 Impact Factor: 1.0 2023 SCImago Journal Rankings: 0.837 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:29Z | - |
dc.date.available | 2019-09-18T08:34:29Z | - |
dc.date.issued | 1997 | - |
dc.identifier.citation | Linear Algebra and Its Applications, 1997, v. 259, n. 1-3, p. 307-327 | - |
dc.identifier.issn | 0024-3795 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276735 | - |
dc.description.abstract | Preconditioned conjugate gradient methods are employed to solve symmetric positive definite m-by-m block Toeplitz with n-by-n Toeplitz block systems Am, nx = b where Am, n are generated by 2π-Periodic nonnegative functions with zeros. Serra has proposed using band block Toeplitz with band Toeplitz block matrices Bm, n, with their external and internal bandwidths independent of m and n as preconditioners. Serra showed that if the Hessians of the generating function at the zeros are positive definite, then the condition number of B-1m, n Am, n is uniformly bounded by a constant independent of m and n, whereas the condition number of Am, n tends to infinity as m and n tend to infinity. In this paper, we provide a method for deriving band preconditioners for block-Toeplitz-Toeplitz-block matrices. Numerical examples are given to illustrate the performance of the method. © Elsevier Science Inc., 1997. | - |
dc.language | eng | - |
dc.relation.ispartof | Linear Algebra and Its Applications | - |
dc.title | Band preconditioners for block-Toeplitz-Toeplitz-block systems | - |
dc.type | Article | - |
dc.description.nature | link_to_OA_fulltext | - |
dc.identifier.doi | 10.1016/S0024-3795(96)00295-9 | - |
dc.identifier.scopus | eid_2-s2.0-0041154571 | - |
dc.identifier.volume | 259 | - |
dc.identifier.issue | 1-3 | - |
dc.identifier.spage | 307 | - |
dc.identifier.epage | 327 | - |
dc.identifier.isi | WOS:A1997XA85000020 | - |
dc.identifier.issnl | 0024-3795 | - |