Publicação
A fast method for solving a block tridiagonal quasi-Toeplitz linear system
| Resumo: | This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by Du, 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 e¤ectiveness of our algorithm in terms of efficiency, stability, and robustness. |
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| Autores principais: | Belhaj, Skander |
| Outros Autores: | Hcini, Fahd; Zhang, Yulin |
| Assunto: | System of linear equations block tridiagonal quasi-Toeplitz matrix block LU decomposition Sherman–Morrison–Woodbury inversion formula |
| Ano: | 2019 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade do Minho |
| Idioma: | inglês |
| Origem: | RepositóriUM - Universidade do Minho |
| Resumo: | This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by Du, 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 e¤ectiveness of our algorithm in terms of efficiency, stability, and robustness. |
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