{"title":"SR分解的精细严格扰动界","authors":"Mahvish Samar, Aamir Farooq","doi":"10.1007/s11766-021-4086-x","DOIUrl":null,"url":null,"abstract":"<div><p>In this article, some new rigorous perturbation bounds for the SR decomposition under normwise or componentwise perturbations for a given matrix are derived. Also, the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach. Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.</p></div>","PeriodicalId":67336,"journal":{"name":"Applied Mathematics-a Journal Of Chinese Universities Series B","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2021-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s11766-021-4086-x.pdf","citationCount":"0","resultStr":"{\"title\":\"Refined rigorous perturbation bounds for the SR decomposition\",\"authors\":\"Mahvish Samar, Aamir Farooq\",\"doi\":\"10.1007/s11766-021-4086-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this article, some new rigorous perturbation bounds for the SR decomposition under normwise or componentwise perturbations for a given matrix are derived. Also, the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach. Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.</p></div>\",\"PeriodicalId\":67336,\"journal\":{\"name\":\"Applied Mathematics-a Journal Of Chinese Universities Series B\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2021-12-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s11766-021-4086-x.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applied Mathematics-a Journal Of Chinese Universities Series B\",\"FirstCategoryId\":\"1089\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s11766-021-4086-x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applied Mathematics-a Journal Of Chinese Universities Series B","FirstCategoryId":"1089","ListUrlMain":"https://link.springer.com/article/10.1007/s11766-021-4086-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Refined rigorous perturbation bounds for the SR decomposition
In this article, some new rigorous perturbation bounds for the SR decomposition under normwise or componentwise perturbations for a given matrix are derived. Also, the explicit expressions for the mixed and componentwise condition numbers are presented by utilizing the block matrix-vector equation approach. Hypothetical and trial results demonstrate that these new bounds are constantly more tightly than the comparing ones in the literature.
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