{"title":"A tridiagonalization-based arbitrary-stride reduction approach for (p,q)-pentadiagonal linear systems","authors":"Yi-Fan Wang, Ji-Teng Jia, Xin Fan","doi":"10.1016/j.apnum.2025.02.017","DOIUrl":null,"url":null,"abstract":"<div><div>As a generalization of pentadiagonal matrices, <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-pentadiagonal matrices have recently attracted considerable interest. In this paper, we first present an arbitrary-stride reduction for block diagonal linear systems composed of <em>M</em>-tridiagonal matrices. Building upon this reduction method and a reliable tridiagonalization process, we propose a tridiagonalization-based arbitrary-stride reduction approach for the <span><math><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></span>-pentadiagonal linear systems. Also, we elucidate eigenvalue clustering of coefficient matrices in the step-by-step process of the stride reduction. Numerical experiments are provided to illustrate the effectiveness of our proposed approach, implementing all experiments using MATLAB programs on a computer.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"213 ","pages":"Pages 77-87"},"PeriodicalIF":2.4000,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Numerical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0168927425000479","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2025/2/25 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
As a generalization of pentadiagonal matrices, -pentadiagonal matrices have recently attracted considerable interest. In this paper, we first present an arbitrary-stride reduction for block diagonal linear systems composed of M-tridiagonal matrices. Building upon this reduction method and a reliable tridiagonalization process, we propose a tridiagonalization-based arbitrary-stride reduction approach for the -pentadiagonal linear systems. Also, we elucidate eigenvalue clustering of coefficient matrices in the step-by-step process of the stride reduction. Numerical experiments are provided to illustrate the effectiveness of our proposed approach, implementing all experiments using MATLAB programs on a computer.
期刊介绍：
The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are:
(i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments.
(ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers.
(iii) Short notes, which present specific new results and techniques in a brief communication.
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