{"title":"On Hermitian positive definite solutions of nonlinear matrix equation","authors":"Qingchun Li, Panpan Liu","doi":"10.1109/ICSSEM.2011.6081228","DOIUrl":null,"url":null,"abstract":"In this paper, the Hermitian positive definite solutions of the nonlinear matrix equations X + A*X<sup>−q</sup>A = Q and X − A*X<sup>−q</sup>A = Q are discussed where q∈(0,1]. Some sufficient conditions for the existence of Hermitian positive definite solutions for these equations are derived. A sufficient condition for X + A*X<sup>−q</sup>A = Q is given to have a unique Hermitian positive definite solution. The perturbation analysis for X − A*X<sup>−q</sup>A = Q is discussed at last.","PeriodicalId":406311,"journal":{"name":"2011 International Conference on System science, Engineering design and Manufacturing informatization","volume":"442 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2011 International Conference on System science, Engineering design and Manufacturing informatization","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICSSEM.2011.6081228","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
In this paper, the Hermitian positive definite solutions of the nonlinear matrix equations X + A*X−qA = Q and X − A*X−qA = Q are discussed where q∈(0,1]. Some sufficient conditions for the existence of Hermitian positive definite solutions for these equations are derived. A sufficient condition for X + A*X−qA = Q is given to have a unique Hermitian positive definite solution. The perturbation analysis for X − A*X−qA = Q is discussed at last.
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