This paper addresses the problem of solving block tridiagonal quasi-Toeplitz linear systems. Inspired by [10], 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.

中文翻译：

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一种求解块三对角拟Toeplitz线性系统的快速方法

本文解决了求解块三对角拟Toeplitz线性系统的问题。受[10]的启发，我们为此类系统提出了一种更通用的算法。该算法基于块三对角拟Toeplitz矩阵的块分解和Sherman-Morrison-Woodbury反演公式。我们还将提议的方法与标准块$ LU $分解方法和高斯算法进行了比较。还提出了理论误差分析。所有算法均已在Matlab中实现。在各种测试问题上进行的数值实验证明了我们算法在效率，稳定性和鲁棒性方面的有效性。