{"title":"非线性矩阵方程的厄米正定解","authors":"Guangyuan Zhao","doi":"10.1109/ICCTD.2009.217","DOIUrl":null,"url":null,"abstract":"In this paper, we study the Hermitian positive definite solutions of the nonlinear matrix equation $X+A* X^{-2} A+I$. Suppose $X$ is a Hermitian positive definite solution of this equation. We discuss the relation between $X$ and $A$ by the eigenvalue and eigenvector of $X$ and $A$ respectively.","PeriodicalId":269403,"journal":{"name":"2009 International Conference on Computer Technology and Development","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2009-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Hermitian Positive Definite Solution of Nonlinear Matrix Equations\",\"authors\":\"Guangyuan Zhao\",\"doi\":\"10.1109/ICCTD.2009.217\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we study the Hermitian positive definite solutions of the nonlinear matrix equation $X+A* X^{-2} A+I$. Suppose $X$ is a Hermitian positive definite solution of this equation. We discuss the relation between $X$ and $A$ by the eigenvalue and eigenvector of $X$ and $A$ respectively.\",\"PeriodicalId\":269403,\"journal\":{\"name\":\"2009 International Conference on Computer Technology and Development\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-11-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 International Conference on Computer Technology and Development\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICCTD.2009.217\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 International Conference on Computer Technology and Development","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICCTD.2009.217","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Hermitian Positive Definite Solution of Nonlinear Matrix Equations
In this paper, we study the Hermitian positive definite solutions of the nonlinear matrix equation $X+A* X^{-2} A+I$. Suppose $X$ is a Hermitian positive definite solution of this equation. We discuss the relation between $X$ and $A$ by the eigenvalue and eigenvector of $X$ and $A$ respectively.
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