{"title":"对称欧几里得距离的显式全局最小化用对称平方实矩阵的表征","authors":"P. Neff, Andreas Fischle, L. Borisov","doi":"10.1137/18M1179663","DOIUrl":null,"url":null,"abstract":"We determine the optimal orthogonal matrices $R \\in {{O}}(n)$ which minimize the symmetrized Euclidean distance $W\\colon {{O}}(n) \\to \\Bbb{R}, \\; W(R\\,;D) \\;:=\\; \\vert\\vert{{sym}(R D - \\mathbbm{1})...","PeriodicalId":48489,"journal":{"name":"SIAM Journal on Applied Algebra and Geometry","volume":"197 1","pages":"31-43"},"PeriodicalIF":1.6000,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":"{\"title\":\"Explicit Global Minimization of the Symmetrized Euclidean Distance by a Characterization of Real Matrices with Symmetric Square\",\"authors\":\"P. Neff, Andreas Fischle, L. Borisov\",\"doi\":\"10.1137/18M1179663\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We determine the optimal orthogonal matrices $R \\\\in {{O}}(n)$ which minimize the symmetrized Euclidean distance $W\\\\colon {{O}}(n) \\\\to \\\\Bbb{R}, \\\\; W(R\\\\,;D) \\\\;:=\\\\; \\\\vert\\\\vert{{sym}(R D - \\\\mathbbm{1})...\",\"PeriodicalId\":48489,\"journal\":{\"name\":\"SIAM Journal on Applied Algebra and Geometry\",\"volume\":\"197 1\",\"pages\":\"31-43\"},\"PeriodicalIF\":1.6000,\"publicationDate\":\"2019-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Applied Algebra and Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/18M1179663\",\"RegionNum\":2,\"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":"SIAM Journal on Applied Algebra and Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/18M1179663","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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