{"title":"广义鞍点线性系统的广义松弛块正半inite分裂预处理器","authors":"Jun Li, Lingsheng Meng, Shu-Xin Miao","doi":"10.1007/s13226-024-00615-2","DOIUrl":null,"url":null,"abstract":"<p>In this paper, based on the block positive-semidefinite splitting (BPS) preconditioner studied recently and the relaxation technique, a generalized relaxed BPS (GRBPS) preconditioner is proposed for generalized saddle point linear system. Spectral properties of the GRBPS preconditioned matrix are analyzed in details. Theoretical results show that the eigenvalues of the preconditioned matrix are clustered at only two points when the iteration parameters are close to zero. Finally, a numerical example is provided to verify the efficiency of the GRBPS preconditioner.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"9 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A generalized relaxed block positive-semidefinite splitting preconditioner for generalized saddle point linear system\",\"authors\":\"Jun Li, Lingsheng Meng, Shu-Xin Miao\",\"doi\":\"10.1007/s13226-024-00615-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, based on the block positive-semidefinite splitting (BPS) preconditioner studied recently and the relaxation technique, a generalized relaxed BPS (GRBPS) preconditioner is proposed for generalized saddle point linear system. Spectral properties of the GRBPS preconditioned matrix are analyzed in details. Theoretical results show that the eigenvalues of the preconditioned matrix are clustered at only two points when the iteration parameters are close to zero. Finally, a numerical example is provided to verify the efficiency of the GRBPS preconditioner.</p>\",\"PeriodicalId\":501427,\"journal\":{\"name\":\"Indian Journal of Pure and Applied Mathematics\",\"volume\":\"9 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-06-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indian Journal of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s13226-024-00615-2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00615-2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A generalized relaxed block positive-semidefinite splitting preconditioner for generalized saddle point linear system
In this paper, based on the block positive-semidefinite splitting (BPS) preconditioner studied recently and the relaxation technique, a generalized relaxed BPS (GRBPS) preconditioner is proposed for generalized saddle point linear system. Spectral properties of the GRBPS preconditioned matrix are analyzed in details. Theoretical results show that the eigenvalues of the preconditioned matrix are clustered at only two points when the iteration parameters are close to zero. Finally, a numerical example is provided to verify the efficiency of the GRBPS preconditioner.
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