{"title":"h矩阵的改进Gauss-Seidel方法的收敛性","authors":"Qingbing Liu","doi":"10.1109/ICNC.2007.317","DOIUrl":null,"url":null,"abstract":"In this paper, we present a new preconditioner which is different from the preconditioner given by Milaszewicz, and prove the monotone convergence theory about this method when the coefficient matrix is an H - matrices. This directly leads to several novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative method.","PeriodicalId":250881,"journal":{"name":"Third International Conference on Natural Computation (ICNC 2007)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2007-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Convergence of the Modified Gauss-Seidel Method for H-matrices\",\"authors\":\"Qingbing Liu\",\"doi\":\"10.1109/ICNC.2007.317\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we present a new preconditioner which is different from the preconditioner given by Milaszewicz, and prove the monotone convergence theory about this method when the coefficient matrix is an H - matrices. This directly leads to several novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative method.\",\"PeriodicalId\":250881,\"journal\":{\"name\":\"Third International Conference on Natural Computation (ICNC 2007)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2007-08-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Third International Conference on Natural Computation (ICNC 2007)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICNC.2007.317\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Third International Conference on Natural Computation (ICNC 2007)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICNC.2007.317","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Convergence of the Modified Gauss-Seidel Method for H-matrices
In this paper, we present a new preconditioner which is different from the preconditioner given by Milaszewicz, and prove the monotone convergence theory about this method when the coefficient matrix is an H - matrices. This directly leads to several novel sufficient conditions for guaranteeing the convergence of the preconditioned iterative method.