基于正弦变换的toeplitz类系统近似逆预调节的改进分析

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics and Computation Pub Date : 2025-06-26 DOI:10.1016/j.amc.2025.129609

Zhi-Wei Fang , Tian-Yi Li , Hai-Wei Sun , Tao Sun

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引用次数: 0

摘要

对于具有对角次Toeplitz结构的非对称线性系统，考虑了一个基于正弦变换的近似逆预条件，其中Toeplitz矩阵是对称正定的。通过对Toeplitz矩阵元素的一些假设，证明了该预条件矩阵的谱位于1附近的有界区间内。这一结果比先前的低秩部分的结果更有力地支持了前置条件的效率，特别是在高维情况下。数值结果验证了该预调节器的有效性。

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Improved analysis of sine-transform-based approximate inverse preconditioner for Toeplitz-like systems

An approximate inverse preconditioner based on sine transform is considered for the nonsymmetric linear systems with diagonal-times-Toeplitz structure, where the Toeplitz matrix is symmetric positive definite. With some assumptions on the elements of the Toeplitz matrix, we proved that the spectra of the preconditioned matrix are located in a bounded interval around one. This result supports the efficiency of the preconditioner more strongly than the former results with low-rank parts, especially in high-dimensional cases. Numerical results are presented to confirm the efficiency of the proposed preconditioner.

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来源期刊

Applied Mathematics and Computation 数学-应用数学

CiteScore

7.90

自引率

10.00%

发文量

755

审稿时长

36 days

期刊介绍： Applied Mathematics and Computation addresses work at the interface between applied mathematics, numerical computation, and applications of systems – oriented ideas to the physical, biological, social, and behavioral sciences, and emphasizes papers of a computational nature focusing on new algorithms, their analysis and numerical results. In addition to presenting research papers, Applied Mathematics and Computation publishes review articles and single–topics issues.