{"title":"关于Sdp秩约简的一个统一定理","authors":"A. M. So, Y. Ye, Jiawei Zhang","doi":"10.1287/moor.1080.0326","DOIUrl":null,"url":null,"abstract":"We consider the problem of finding a low{rank approximate solution to a system of linearequations in symmetric, positive semidefinite matrices. Specifically, let A1; : : : ;Am 2 Rn£n symmetric, positive semidefinite matrices, and let b1; : : : ; bm ¸ 0. We show that if there exists a symmetric, positive semidefinite matrix X to the following system of equations:","PeriodicalId":124312,"journal":{"name":"New York University Stern School of Business Research Paper Series","volume":"75 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"72","resultStr":"{\"title\":\"A Unified Theorem on Sdp Rank Reduction\",\"authors\":\"A. M. So, Y. Ye, Jiawei Zhang\",\"doi\":\"10.1287/moor.1080.0326\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of finding a low{rank approximate solution to a system of linearequations in symmetric, positive semidefinite matrices. Specifically, let A1; : : : ;Am 2 Rn£n symmetric, positive semidefinite matrices, and let b1; : : : ; bm ¸ 0. We show that if there exists a symmetric, positive semidefinite matrix X to the following system of equations:\",\"PeriodicalId\":124312,\"journal\":{\"name\":\"New York University Stern School of Business Research Paper Series\",\"volume\":\"75 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"72\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"New York University Stern School of Business Research Paper Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1287/moor.1080.0326\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"New York University Stern School of Business Research Paper Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1287/moor.1080.0326","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We consider the problem of finding a low{rank approximate solution to a system of linearequations in symmetric, positive semidefinite matrices. Specifically, let A1; : : : ;Am 2 Rn£n symmetric, positive semidefinite matrices, and let b1; : : : ; bm ¸ 0. We show that if there exists a symmetric, positive semidefinite matrix X to the following system of equations:
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