{"title":"Highly accurate verified error bounds for Krylov type linear system solvers","authors":"Axel Facius","doi":"10.1016/S0168-9274(02)00234-9","DOIUrl":null,"url":null,"abstract":"<div><div>Preconditioned Krylov subspace solvers are an important and frequently used technique for solving large sparse linear systems. There are many advantageous properties concerning convergence rates and error estimates. However, implementing such a solver on a computer, we often observe an unexpected and even contrary behavior.</div><div>The purpose of this paper is to show that this gap between the theoretical and practical behavior can be narrowed by using a problem-oriented arithmetic. In addition we give rigorous error bounds to our computed results.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"45 1","pages":"Pages 41-58"},"PeriodicalIF":2.4000,"publicationDate":"2003-04-01","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/S0168927402002349","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2003/2/8 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
Preconditioned Krylov subspace solvers are an important and frequently used technique for solving large sparse linear systems. There are many advantageous properties concerning convergence rates and error estimates. However, implementing such a solver on a computer, we often observe an unexpected and even contrary behavior.
The purpose of this paper is to show that this gap between the theoretical and practical behavior can be narrowed by using a problem-oriented arithmetic. In addition we give rigorous error bounds to our computed results.
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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