Using the Sherman-Morrison-Woodbury inversion formula for a fast solution of tridiagonal block Toeplitz systems |
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Authors: | Alexander Malyshev Miloud Sadkane |
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Affiliation: | a Department of Mathematics, University of Bergen, Post Box 7803, 5020 Bergen, Norway b Université de Brest, Laboratoire de Mathématiques, CNRS - UMR 6205, 6 Av. Le Gorgeu, 29238 Brest Cedex 3, France |
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Abstract: | A fast numerical algorithm for solving systems of linear equations with tridiagonal block Toeplitz matrices is presented. The algorithm is based on a preliminary factorization of the generating quadratic matrix polynomial associated with the Toeplitz matrix, followed by the Sherman-Morrison-Woodbury inversion formula and solution of two bidiagonal and one diagonal block Toeplitz systems. Tight estimates of the condition numbers are provided for the matrix system and the main matrix systems generated during the preliminary factorization. The emphasis is put on rigorous stability analysis to rounding errors of the Sherman-Morrison-Woodbury inversion. Numerical experiments are provided to illustrate the theory. |
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Keywords: | 65F05 15B05 15A23 |
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