求解大型非对称线性系统的改进CMRH方法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-07-08 DOI:10.1016/j.aml.2025.109672

Qianqian Xue, Wenli Zeng, Xiaoqi Xu, Xian-Ming Gu

{"title":"求解大型非对称线性系统的改进CMRH方法","authors":"Qianqian Xue, Wenli Zeng, Xiaoqi Xu, Xian-Ming Gu","doi":"10.1016/j.aml.2025.109672","DOIUrl":null,"url":null,"abstract":"<div><div>This paper presents a modified CMRH method for solving large nonsymmetric linear systems. Based on the Hessenberg process, the proposed method requires less computation and storage compared to GMRES and QMR methods. The improvement involves utilizing the <span><math><mrow><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-th vector generated during the Hessenberg process to optimize the approximate solution through a linear combination, thereby reducing the number of matrix–vector multiplications and inner products. Theoretical analysis demonstrates that the improved CMRH method is more cost-effective than the original <span><math><mrow><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-step method. Numerical experiments validate the efficiency of the modified CMRH method across various test problems, showing fewer iterations and less computation time, particularly in large-scale problems.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109672"},"PeriodicalIF":2.8000,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A modified CMRH method for solving large nonsymmetric linear systems\",\"authors\":\"Qianqian Xue, Wenli Zeng, Xiaoqi Xu, Xian-Ming Gu\",\"doi\":\"10.1016/j.aml.2025.109672\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>This paper presents a modified CMRH method for solving large nonsymmetric linear systems. Based on the Hessenberg process, the proposed method requires less computation and storage compared to GMRES and QMR methods. The improvement involves utilizing the <span><math><mrow><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-th vector generated during the Hessenberg process to optimize the approximate solution through a linear combination, thereby reducing the number of matrix–vector multiplications and inner products. Theoretical analysis demonstrates that the improved CMRH method is more cost-effective than the original <span><math><mrow><mo>(</mo><mi>m</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow></math></span>-step method. Numerical experiments validate the efficiency of the modified CMRH method across various test problems, showing fewer iterations and less computation time, particularly in large-scale problems.</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"171 \",\"pages\":\"Article 109672\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2025-07-08\",\"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/S0893965925002228\",\"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/S0893965925002228","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

本文提出了求解大型非对称线性系统的改进CMRH方法。该方法基于Hessenberg过程，与GMRES和QMR方法相比，计算量和存储空间更小。改进包括利用在Hessenberg过程中生成的(m+1)-th向量通过线性组合优化近似解，从而减少矩阵-向量乘法和内积的数量。理论分析表明，改进的CMRH方法比原（m+1）步法具有更高的成本效益。数值实验验证了改进的CMRH方法在各种测试问题中的有效性，特别是在大规模问题中，迭代次数更少，计算时间更短。

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 modified CMRH method for solving large nonsymmetric linear systems

This paper presents a modified CMRH method for solving large nonsymmetric linear systems. Based on the Hessenberg process, the proposed method requires less computation and storage compared to GMRES and QMR methods. The improvement involves utilizing the

(m + 1)

-th vector generated during the Hessenberg process to optimize the approximate solution through a linear combination, thereby reducing the number of matrix–vector multiplications and inner products. Theoretical analysis demonstrates that the improved CMRH method is more cost-effective than the original

(m + 1)

-step method. Numerical experiments validate the efficiency of the modified CMRH method across various test problems, showing fewer iterations and less computation time, particularly in large-scale problems.

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.