This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by , 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 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.
Cite this article
Skander Belhaj, Fahd Hcini, Yulin Zhang, A fast method for solving a block tridiagonal quasi-Toeplitz linear system. Port. Math. 76 (2019), no. 3/4, pp. 287–299DOI 10.4171/PM/2036