{"title":"非线性矩阵方程的厄米正定解","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":"{\"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}","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}
On Hermitian positive definite solutions of nonlinear matrix equation
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
