{"title":"Improved error bounds for the deflated multi-preconditioned CG method","authors":"Reinhard Nabben, Julian Schramm","doi":"10.1016/j.laa.2025.02.022","DOIUrl":null,"url":null,"abstract":"<div><div>Preconditioning and deflation are well-known techniques to speed up the convergence of the CG method. The concept of multiple-preconditioning however is introduced in the last decade. Recently, in <span><span>[21]</span></span>, a new adaptive preconditioned CG method is established that combines all these techniques. The main tool of the adaptive method is a new error bound for the deflated preconditioned CG method. Using this bound it is decided in each iteration if the deflated preconditioned CG method is sufficient in reducing the error or whether an acceleration by performing iterations of the multi-preconditioned CG method is needed. Here we improve this error bound. This new bound contributes to the theory of deflation methods but can also lead to new decision rules for the adaptive multi-preconditioned CG method.</div></div>","PeriodicalId":18043,"journal":{"name":"Linear Algebra and its Applications","volume":"712 ","pages":"Pages 29-48"},"PeriodicalIF":1.0000,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Linear Algebra and its Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0024379525000795","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Preconditioning and deflation are well-known techniques to speed up the convergence of the CG method. The concept of multiple-preconditioning however is introduced in the last decade. Recently, in [21], a new adaptive preconditioned CG method is established that combines all these techniques. The main tool of the adaptive method is a new error bound for the deflated preconditioned CG method. Using this bound it is decided in each iteration if the deflated preconditioned CG method is sufficient in reducing the error or whether an acceleration by performing iterations of the multi-preconditioned CG method is needed. Here we improve this error bound. This new bound contributes to the theory of deflation methods but can also lead to new decision rules for the adaptive multi-preconditioned CG method.
期刊介绍：
Linear Algebra and its Applications publishes articles that contribute new information or new insights to matrix theory and finite dimensional linear algebra in their algebraic, arithmetic, combinatorial, geometric, or numerical aspects. It also publishes articles that give significant applications of matrix theory or linear algebra to other branches of mathematics and to other sciences. Articles that provide new information or perspectives on the historical development of matrix theory and linear algebra are also welcome. Expository articles which can serve as an introduction to a subject for workers in related areas and which bring one to the frontiers of research are encouraged. Reviews of books are published occasionally as are conference reports that provide an historical record of major meetings on matrix theory and linear algebra.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
