{"title":"块三乘三鞍点问题的改进交替正半定分裂预条件","authors":"Fang Chen, Bijun Ren","doi":"10.1553/etna_vol58s84","DOIUrl":null,"url":null,"abstract":"We propose a modified alternating positive semidefinite splitting (MAPSS) preconditioner for solving block three-by-three saddle point problems that arise in linear programming and the finite element discretization of Maxwell equations. Spectral properties of the MAPSS-preconditioned matrix are discussed and analyzed in detail. As the efficiency of the MAPSS preconditioner depends on its parameters, we derive fast and effective formulas to compute the quasi-optimal values of these parameters. Numerical examples show that the MAPSS preconditioner performs better than the APSS preconditioner.","PeriodicalId":282695,"journal":{"name":"ETNA - Electronic Transactions on Numerical Analysis","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A modified alternating positive semidefinite splitting preconditioner for block three-by-three saddle point problems\",\"authors\":\"Fang Chen, Bijun Ren\",\"doi\":\"10.1553/etna_vol58s84\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose a modified alternating positive semidefinite splitting (MAPSS) preconditioner for solving block three-by-three saddle point problems that arise in linear programming and the finite element discretization of Maxwell equations. Spectral properties of the MAPSS-preconditioned matrix are discussed and analyzed in detail. As the efficiency of the MAPSS preconditioner depends on its parameters, we derive fast and effective formulas to compute the quasi-optimal values of these parameters. Numerical examples show that the MAPSS preconditioner performs better than the APSS preconditioner.\",\"PeriodicalId\":282695,\"journal\":{\"name\":\"ETNA - Electronic Transactions on Numerical Analysis\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ETNA - Electronic Transactions on Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1553/etna_vol58s84\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ETNA - Electronic Transactions on Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1553/etna_vol58s84","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A modified alternating positive semidefinite splitting preconditioner for block three-by-three saddle point problems
We propose a modified alternating positive semidefinite splitting (MAPSS) preconditioner for solving block three-by-three saddle point problems that arise in linear programming and the finite element discretization of Maxwell equations. Spectral properties of the MAPSS-preconditioned matrix are discussed and analyzed in detail. As the efficiency of the MAPSS preconditioner depends on its parameters, we derive fast and effective formulas to compute the quasi-optimal values of these parameters. Numerical examples show that the MAPSS preconditioner performs better than the APSS preconditioner.
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