{"title":"Flexible and multi-shift induced dimension reduction algorithms for solving large sparse linear systems","authors":"M. Gijzen, G. Sleijpen, J. Zemke","doi":"10.15480/882.1019","DOIUrl":null,"url":null,"abstract":"We give two important generalizations of the Induced Dimension Reduction (IDR) approach for the solution of linear systems. We derive a flexible and a multi-shift Quasi-Minimal Residual IDR (QMRIDR) variant. Numerical examples are presented to show the effectiveness of these new IDR variants compared to existing ones and to other Krylov subspace methods","PeriodicalId":266346,"journal":{"name":"Reports of the Department of Applied Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2011-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"25","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Reports of the Department of Applied Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15480/882.1019","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 25
Abstract
We give two important generalizations of the Induced Dimension Reduction (IDR) approach for the solution of linear systems. We derive a flexible and a multi-shift Quasi-Minimal Residual IDR (QMRIDR) variant. Numerical examples are presented to show the effectiveness of these new IDR variants compared to existing ones and to other Krylov subspace methods