对角加非对称Toeplitz线性系统的无条件收敛CSCS迭代方法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-05-28 DOI:10.1016/j.aml.2025.109631

Zi-Hang She , Qiu-Ya Wang , Zhibo Wang

{"title":"对角加非对称Toeplitz线性系统的无条件收敛CSCS迭代方法","authors":"Zi-Hang She , Qiu-Ya Wang , Zhibo Wang","doi":"10.1016/j.aml.2025.109631","DOIUrl":null,"url":null,"abstract":"<div><div>This article is dedicated to developing a circulant and skew-circulant splitting (CSCS) iterative method for addressing a specific class of diagonal-plus-asymmetric Toeplitz systems. Theoretically, we have analyzed that the spectral radius of the convergence factor of the proposed CSCS iterative method is strictly less than 1, which implies the unconditional convergence of the proposed iterative method. Moreover, we derive an upper bound of the contraction factor of the CSCS iteration. This upper bound is dependent on two factors: the spectra of the circulant and the skew-circulant matrices, and the range of values for the elements in the diagonal matrix involved. Numerical results are provided to demonstrate the effectiveness of the proposed iterative method.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109631"},"PeriodicalIF":2.8000,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An unconditionally convergent CSCS iterative method for diagonal-plus-asymmetric Toeplitz linear systems\",\"authors\":\"Zi-Hang She , Qiu-Ya Wang , Zhibo Wang\",\"doi\":\"10.1016/j.aml.2025.109631\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This article is dedicated to developing a circulant and skew-circulant splitting (CSCS) iterative method for addressing a specific class of diagonal-plus-asymmetric Toeplitz systems. Theoretically, we have analyzed that the spectral radius of the convergence factor of the proposed CSCS iterative method is strictly less than 1, which implies the unconditional convergence of the proposed iterative method. Moreover, we derive an upper bound of the contraction factor of the CSCS iteration. This upper bound is dependent on two factors: the spectra of the circulant and the skew-circulant matrices, and the range of values for the elements in the diagonal matrix involved. Numerical results are provided to demonstrate the effectiveness of the proposed iterative method.</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"171 \",\"pages\":\"Article 109631\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2025-05-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0893965925001818\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics Letters","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0893965925001818","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

本文致力于开发一种循环和斜循环分裂（CSCS）迭代方法来处理一类特定的对角加非对称Toeplitz系统。理论上，我们分析了所提出的CSCS迭代方法收敛因子的谱半径严格小于1，这意味着所提出的迭代方法是无条件收敛的。此外，我们还得到了CSCS迭代收缩因子的上界。这个上界取决于两个因素：循环矩阵和斜循环矩阵的谱，以及所涉及的对角矩阵中元素的取值范围。数值结果验证了所提迭代方法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

An unconditionally convergent CSCS iterative method for diagonal-plus-asymmetric Toeplitz linear systems

This article is dedicated to developing a circulant and skew-circulant splitting (CSCS) iterative method for addressing a specific class of diagonal-plus-asymmetric Toeplitz systems. Theoretically, we have analyzed that the spectral radius of the convergence factor of the proposed CSCS iterative method is strictly less than 1, which implies the unconditional convergence of the proposed iterative method. Moreover, we derive an upper bound of the contraction factor of the CSCS iteration. This upper bound is dependent on two factors: the spectra of the circulant and the skew-circulant matrices, and the range of values for the elements in the diagonal matrix involved. Numerical results are provided to demonstrate the effectiveness of the proposed iterative method.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.