求解不定最小二乘问题的交替方向隐式迭代法

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-07-09 DOI:10.1016/j.aml.2025.109677

Lingsheng Meng, Peizhe Li, Kailiang Xin

{"title":"求解不定最小二乘问题的交替方向隐式迭代法","authors":"Lingsheng Meng, Peizhe Li, Kailiang Xin","doi":"10.1016/j.aml.2025.109677","DOIUrl":null,"url":null,"abstract":"<div><div>To solve the indefinite least squares problem, first we propose the generalized splitting iterative method, which is unconditionally convergent. Further, to accelerate the generalized splitting iterative method, we propose the alternating direction implicit iterative method, which needs to satisfy condition to guarantee convergence. Numerical experiments show that the alternating direction implicit iterative method outperforms the current methods in terms of CPU time and number of iteration steps.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"171 ","pages":"Article 109677"},"PeriodicalIF":2.8000,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Alternating direction implicit iterative method for solving indefinite least squares problem\",\"authors\":\"Lingsheng Meng, Peizhe Li, Kailiang Xin\",\"doi\":\"10.1016/j.aml.2025.109677\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>To solve the indefinite least squares problem, first we propose the generalized splitting iterative method, which is unconditionally convergent. Further, to accelerate the generalized splitting iterative method, we propose the alternating direction implicit iterative method, which needs to satisfy condition to guarantee convergence. Numerical experiments show that the alternating direction implicit iterative method outperforms the current methods in terms of CPU time and number of iteration steps.</div></div>\",\"PeriodicalId\":55497,\"journal\":{\"name\":\"Applied Mathematics Letters\",\"volume\":\"171 \",\"pages\":\"Article 109677\"},\"PeriodicalIF\":2.8000,\"publicationDate\":\"2025-07-09\",\"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/S0893965925002277\",\"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/S0893965925002277","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

为了求解不定最小二乘问题，首先提出了无条件收敛的广义分裂迭代法。进一步，为了加快广义分裂迭代法的求解速度，提出了交替方向隐式迭代法，该方法需要满足保证收敛的条件。数值实验表明，交替方向隐式迭代法在CPU时间和迭代步数方面优于现有方法。

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

Alternating direction implicit iterative method for solving indefinite least squares problem

To solve the indefinite least squares problem, first we propose the generalized splitting iterative method, which is unconditionally convergent. Further, to accelerate the generalized splitting iterative method, we propose the alternating direction implicit iterative method, which needs to satisfy condition to guarantee convergence. Numerical experiments show that the alternating direction implicit iterative method outperforms the current methods in terms of CPU time and number of iteration steps.

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.