A fast method for solving a block tridiagonal quasi-Toeplitz linear system (Q2211438)

Summary: This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by [\textit{L. Du} et al., Appl. Math. Lett. 75, 74--81 (2018; Zbl 1377.65037)], 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 effectiveness of our algorithm in terms of efficiency, stability and robustness.