Algorithms for solving a class of real quasi-symmetric Toeplitz linear systems and its applications

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.3934/era.2023101

Xinglong Zhang, Xiaoyu Jiang, Zhaolin Jiang, Hee-Young Byun

引用次数: 0

Abstract

In this paper, fast numerical methods for solving the real quasi-symmetric Toeplitz linear system are studied in two stages. First, based on an order-reduction algorithm and the factorization of Toeplitz matrix inversion, a sequence of linear systems with a constant symmetric Toeplitz matrix are solved. Second, two new fast algorithms are employed to solve the real quasi-symmetric Toeplitz linear system. Furthermore, we show a fast algorithm for quasi-symmetric Toeplitz matrix-vector multiplication. In addition, the stability analysis of the splitting symmetric Toeplitz inversion is discussed. In mathematical or engineering problems, the proposed algorithms are extraordinarily effective for solving a sequence of linear systems with a constant symmetric Toeplitz matrix. Fast matrix-vector multiplication and a quasi-symmetric Toeplitz linear solver are proven to be suitable for image encryption and decryption.

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一类实拟对称Toeplitz线性系统的求解算法及其应用

本文分两个阶段研究了求解实拟对称Toeplitz线性系统的快速数值方法。首先，基于降阶算法和Toeplitz矩阵逆分解，求解了一类具有常对称Toeplitz矩阵的线性系统序列。其次，采用两种新的快速算法求解拟对称Toeplitz线性方程组。此外，我们给出了一个准对称Toeplitz矩阵向量乘法的快速算法。此外，还讨论了分裂对称Toeplitz反演的稳定性分析。在数学或工程问题中，所提出的算法对于求解具有恒定对称Toeplitz矩阵的线性系统序列非常有效。证明了快速矩阵向量乘法和准对称Toeplitz线性解算器适用于图像加解密。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.