A fast method for solving a block tridiagonal quasi-Toeplitz linear system

Abstract

. 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.