A fast method for solving a block tridiagonal quasi-Toeplitz linear system
This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by [10], we propose a more general algorithm for such systems. The algorithm is based on a block decomposition for block tridiagonal quasi-Toeplitz matrices and the Sherman–Morrison–Woodbury inversi...
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| Veröffentlicht in: | Portugaliae mathematica 2019-01, Vol.76 (3), p.287-299 |
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| container_title | Portugaliae mathematica |
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| creator | Belhaj, Skander Hcini, Fahd Zhang, Yulin |
| description | This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by [10], we propose a more general algorithm for such systems. The algorithm is based on a block decomposition for block tridiagonal quasi-Toeplitz matrices and the Sherman–Morrison–Woodbury inversion formula. We also compare the proposed approach to the standard block $LU$ decomposition method and the Gauss algorithm. A theoretical error analysis is also presented. All algorithms have been implemented in Matlab. Numerical experiments performed on a wide variety of test problems show the effectiveness of our algorithm in terms of efficiency, stability and robustness. |
| doi_str_mv | 10.4171/PM/2036 |
| format | Article |
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Math</addtitle><description>This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by [10], we propose a more general algorithm for such systems. The algorithm is based on a block decomposition for block tridiagonal quasi-Toeplitz matrices and the Sherman–Morrison–Woodbury inversion formula. We also compare the proposed approach to the standard block $LU$ decomposition method and the Gauss algorithm. A theoretical error analysis is also presented. All algorithms have been implemented in Matlab. 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Math</addtitle><date>2019-01-01</date><risdate>2019</risdate><volume>76</volume><issue>3</issue><spage>287</spage><epage>299</epage><pages>287-299</pages><issn>0032-5155</issn><eissn>1662-2758</eissn><abstract>This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by [10], we propose a more general algorithm for such systems. The algorithm is based on a block decomposition for block tridiagonal quasi-Toeplitz matrices and the Sherman–Morrison–Woodbury inversion formula. We also compare the proposed approach to the standard block $LU$ decomposition method and the Gauss algorithm. A theoretical error analysis is also presented. All algorithms have been implemented in Matlab. Numerical experiments performed on a wide variety of test problems show the effectiveness of our algorithm in terms of efficiency, stability and robustness.</abstract><cop>Zuerich, Switzerland</cop><pub>European Mathematical Society Publishing House</pub><doi>10.4171/PM/2036</doi><tpages>13</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Portugaliae mathematica, 2019-01, Vol.76 (3), p.287-299 |
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| source | European Mathematical Society Publishing House |
| subjects | block LU decomposition Ciências Naturais Linear and multilinear algebra Matemáticas matrix theory Numerical analysis Science & Technology Sherman–Morrison–Woodbury inversion formula System of linear equations |
| title | A fast method for solving a block tridiagonal quasi-Toeplitz linear system |
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