求解复杂对称线性方程的双参数双步分裂迭代法

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics Pub Date : 2024-04-05 DOI:10.21136/AM.2024.0133-23

Beibei Li, Jingjing Cui, Zhengge Huang, Xiaofeng Xie

{"title":"求解复杂对称线性方程的双参数双步分裂迭代法","authors":"Beibei Li, Jingjing Cui, Zhengge Huang, Xiaofeng Xie","doi":"10.21136/AM.2024.0133-23","DOIUrl":null,"url":null,"abstract":"<div><p>We multiply both sides of the complex symmetric linear system <i>Ax</i> = <i>b</i> by 1 − i<i>ω</i> to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 3","pages":"311 - 337"},"PeriodicalIF":0.6000,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations\",\"authors\":\"Beibei Li, Jingjing Cui, Zhengge Huang, Xiaofeng Xie\",\"doi\":\"10.21136/AM.2024.0133-23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We multiply both sides of the complex symmetric linear system <i>Ax</i> = <i>b</i> by 1 − i<i>ω</i> to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed method.</p></div>\",\"PeriodicalId\":55505,\"journal\":{\"name\":\"Applications of Mathematics\",\"volume\":\"69 3\",\"pages\":\"311 - 337\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applications of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.21136/AM.2024.0133-23\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applications of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.21136/AM.2024.0133-23","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

我们将复对称线性系统 Ax = b 的两边乘以 1 - iω，得到一个新的等效线性系统，然后建立了一个双参数双步分裂（DDSS）方法来求解新的线性系统。此外，我们还提出了 DDSS 方法迭代矩阵谱半径的上界，并获得了其准最优参数。理论分析表明，当满足某些条件时，新方法是收敛的。我们还给出了一些测试实例来说明所提方法的有效性。

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

A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations

We multiply both sides of the complex symmetric linear system Ax = b by 1 − iω to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are given to illustrate the effectiveness of the proposed 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

Applications of Mathematics 数学-应用数学

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering. The main topics covered include: - Mechanics of Solids; - Fluid Mechanics; - Electrical Engineering; - Solutions of Differential and Integral Equations; - Mathematical Physics; - Optimization; - Probability Mathematical Statistics. The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.