On Hermitian positive definite solution of nonlinear matrix equation X plus A* X-2 A = Q

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	*On Hermitian positive definite solution of nonlinear matrix equation X plus A X-2 A = Q**
	Guo, XX
	2005-09-01
发表期刊	JOURNAL OF COMPUTATIONAL MATHEMATICS
ISSN	0254-9409
卷号	23 期号:5 页码:513-526
摘要	Based on the fixed-point theory, we study the existence and the uniqueness of the maximal Hermitian positive definite solution of the nonlinear matrix equation X + A* X-2 A = Q, where Q is a square Hermitian positive definite matrix and A* is the conjugate transpose of the matrix A. We also demonstrate some essential properties and analyze the sensitivity of this solution. In addition, we derive computable error bounds about the approximations to the maximal Hermitian positive definite solution of the nonlinear matrix equation X + A* X-2 A = Q. At last, we further generalize these results to the nonlinear matrix equation X + A* X-n A = Q, where n >= 2 is a given positive integer.
关键词	nonlinear matrix equation Hermitian positive definite solution sensitivity analysis error bound
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000232012900006
出版者	VSP BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/1042
专题	中国科学院数学与系统科学研究院
通讯作者	Guo, XX
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Guo, XX. On Hermitian positive definite solution of nonlinear matrix equation X plus A* X-2 A = Q[J]. JOURNAL OF COMPUTATIONAL MATHEMATICS,2005,23(5):513-526.
APA	Guo, XX.(2005).On Hermitian positive definite solution of nonlinear matrix equation X plus A* X-2 A = Q.JOURNAL OF COMPUTATIONAL MATHEMATICS,23(5),513-526.
MLA	Guo, XX."On Hermitian positive definite solution of nonlinear matrix equation X plus A* X-2 A = Q".JOURNAL OF COMPUTATIONAL MATHEMATICS 23.5(2005):513-526.