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 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.