求解块三对角拟Toeplitz线性系统的一种快速方法

IF 0.5 4区数学 Q3 MATHEMATICS

Portugaliae Mathematica Pub Date : 2020-07-15 DOI:10.4171/pm/2036

S. Belhaj, Fahd Hcini, Yulin Zhang

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引用次数: 3

摘要

．本文研究了块三对角拟toeplitz线性系统的求解问题。受[9]的启发，我们提出了一个更广义的算法。该算法基于块三对角拟toeplitz矩阵的分块分解和Sherman-Morrison-Woodbury反演公式。我们还将所提出的方法与标准块逻辑单元分解方法进行了比较。并对理论精度和误差进行了分析。所有算法都在Matlab中实现。对各种测试问题进行的数值实验表明，我们的算法在效率、稳定性和鲁棒性方面是有效的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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

. 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.

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来源期刊

Portugaliae Mathematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

0.90

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： Since its foundation in 1937, Portugaliae Mathematica has aimed at publishing high-level research articles in all branches of mathematics. With great efforts by its founders, the journal was able to publish articles by some of the best mathematicians of the time. In 2001 a New Series of Portugaliae Mathematica was started, reaffirming the purpose of maintaining a high-level research journal in mathematics with a wide range scope.