This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by [9], we propose a more generalized algorithm for such systems. The algorithm is based on a block decomposition for a block tridiagonal quasi-Toeplitz matrix and the Sherman-Morrison-Woodbury inversion formula. We also compare the proposed approach to the standard block LU decomposition method. A theoretical accuracy and error analysis is also considered. All algorithms have been implemented in Matlab. Numerical experiments performed with a wide variety of test problems show the effectiveness of our algorithm in terms of efficience, stability and robustness.
In this paper, we develop a new algorithm for solving diagonally dominant symmetric quasi-pentadiagonal Toeplitz linear systems. Numerical experiments are given in order to illustrate the validity and efficiency of our algorithm.
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