{"title":"三角矩阵的连续奇异值分解Jacobi方法的二次收敛性","authors":"V. Hari","doi":"10.1137/0910065","DOIUrl":null,"url":null,"abstract":"The quadratic convergence of the serial singular value decomposition (SVD) Jacobi methods for triangular matrices is proved. The obtained bounds are as sharp as those obtained by Wilkinson and Van Kempen for the symmetric Jacobi method. Special attention is paid to finding the structure of almost diagonal essentially triangular matrices with multiple singular values.","PeriodicalId":200176,"journal":{"name":"Siam Journal on Scientific and Statistical Computing","volume":"99 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1989-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"On the quadratic convergence of the serial singular value decomposition Jacobi methods for triangular matrices\",\"authors\":\"V. Hari\",\"doi\":\"10.1137/0910065\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The quadratic convergence of the serial singular value decomposition (SVD) Jacobi methods for triangular matrices is proved. The obtained bounds are as sharp as those obtained by Wilkinson and Van Kempen for the symmetric Jacobi method. Special attention is paid to finding the structure of almost diagonal essentially triangular matrices with multiple singular values.\",\"PeriodicalId\":200176,\"journal\":{\"name\":\"Siam Journal on Scientific and Statistical Computing\",\"volume\":\"99 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1989-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siam Journal on Scientific and Statistical Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1137/0910065\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siam Journal on Scientific and Statistical Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1137/0910065","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the quadratic convergence of the serial singular value decomposition Jacobi methods for triangular matrices
The quadratic convergence of the serial singular value decomposition (SVD) Jacobi methods for triangular matrices is proved. The obtained bounds are as sharp as those obtained by Wilkinson and Van Kempen for the symmetric Jacobi method. Special attention is paid to finding the structure of almost diagonal essentially triangular matrices with multiple singular values.