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- Publisher Website: 10.1007/s11075-009-9335-7
- Scopus: eid_2-s2.0-77952010244
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Article: Inverse product Toeplitz preconditioners for non-Hermitian Toeplitz systems
Title | Inverse product Toeplitz preconditioners for non-Hermitian Toeplitz systems |
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Authors | |
Keywords | Rational function Toeplitz matrix Generating function GMRES |
Issue Date | 2010 |
Citation | Numerical Algorithms, 2010, v. 54, n. 2, p. 279-295 How to Cite? |
Abstract | In this paper, we first propose product Toeplitz preconditioners (in an inverse form) for non-Hermitian Toeplitz matrices generated by functions with zeros. Our inverse product-type preconditioner is of the form T F T L-1 T U-1 where T F , T L , and T U are full, band lower triangular, and band upper triangular Toeplitz matrices, respectively. Our basic idea is to decompose the generating function properly such that all factors T F , T L , and T U of the preconditioner are as well-conditioned as possible. We prove that under certain conditions, the preconditioned matrix has eigenvalues and singular values clustered around 1. Then we use a similar idea to modify the preconditioner proposed in Ku and Kuo (SIAM J Sci Stat Comput 13:1470-1487, 1992) to handle the zeros in rational generating functions. Numerical results, including applications to the computation of the stationary probability distribution of Markovian queuing models with batch arrival, are given to illustrate the good performance of the proposed preconditioners. © 2009 Springer Science+Business Media, LLC. |
Persistent Identifier | http://hdl.handle.net/10722/276860 |
ISSN | 2023 Impact Factor: 1.7 2023 SCImago Journal Rankings: 0.829 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Lin, Fu Rong | - |
dc.contributor.author | Ng, Michael K. | - |
dc.date.accessioned | 2019-09-18T08:34:52Z | - |
dc.date.available | 2019-09-18T08:34:52Z | - |
dc.date.issued | 2010 | - |
dc.identifier.citation | Numerical Algorithms, 2010, v. 54, n. 2, p. 279-295 | - |
dc.identifier.issn | 1017-1398 | - |
dc.identifier.uri | http://hdl.handle.net/10722/276860 | - |
dc.description.abstract | In this paper, we first propose product Toeplitz preconditioners (in an inverse form) for non-Hermitian Toeplitz matrices generated by functions with zeros. Our inverse product-type preconditioner is of the form T F T L-1 T U-1 where T F , T L , and T U are full, band lower triangular, and band upper triangular Toeplitz matrices, respectively. Our basic idea is to decompose the generating function properly such that all factors T F , T L , and T U of the preconditioner are as well-conditioned as possible. We prove that under certain conditions, the preconditioned matrix has eigenvalues and singular values clustered around 1. Then we use a similar idea to modify the preconditioner proposed in Ku and Kuo (SIAM J Sci Stat Comput 13:1470-1487, 1992) to handle the zeros in rational generating functions. Numerical results, including applications to the computation of the stationary probability distribution of Markovian queuing models with batch arrival, are given to illustrate the good performance of the proposed preconditioners. © 2009 Springer Science+Business Media, LLC. | - |
dc.language | eng | - |
dc.relation.ispartof | Numerical Algorithms | - |
dc.subject | Rational function | - |
dc.subject | Toeplitz matrix | - |
dc.subject | Generating function | - |
dc.subject | GMRES | - |
dc.title | Inverse product Toeplitz preconditioners for non-Hermitian Toeplitz systems | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s11075-009-9335-7 | - |
dc.identifier.scopus | eid_2-s2.0-77952010244 | - |
dc.identifier.volume | 54 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 279 | - |
dc.identifier.epage | 295 | - |
dc.identifier.eissn | 1572-9265 | - |
dc.identifier.isi | WOS:000277203600006 | - |
dc.identifier.issnl | 1017-1398 | - |