Least-squares solution of inverse problem for hermitian anti-reflexive matrices and its appoximation

doi:10.1007/s10114-005-0549-x

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	Least-squares solution of inverse problem for hermitian anti-reflexive matrices and its appoximation
	Peng, ZY ; Deng, YB ; Liu, JW
	2006-04-01
发表期刊	ACTA MATHEMATICA SINICA-ENGLISH SERIES
ISSN	1439-8516
卷号	22 期号:2 页码:477-484
摘要	In this paper, we first consider the least-squares solution of the matrix inverse problem as follows: Find a hermitian anti-reflexive matrix corresponding to a given generalized reflection matrix J such that for given matrices X,B we have min(A) parallel to CuAX -B parallel to. The existence theorems are obtained, and a general representation of such a matrix is presented. We denote the set of such matrices by S(E). Then the matrix nearness problem for the matrix inverse problem is discussed. That is: Given an arbitrary A, find a matrix (A) over cap is an element of SE which is nearest to A in Frobenius norm. We show that the nearest matrix is unique and provide an expression for this nearest matrix.
关键词	hermitian reflexive matrix hermitian anti-reflexive matrix matrix norm nearest matrix
DOI	10.1007/s10114-005-0549-x
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000235927700017
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/3019
专题	中国科学院数学与系统科学研究院
通讯作者	Peng, ZY
作者单位	1.Hunan Univ Sci & Technol, Dept Math, Xiangtan 411201, Peoples R China 2.Cent S Univ, Dept Math, Changsha 410083, Peoples R China 3.Chinese Acad Sci, Inst Computat Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Peng, ZY,Deng, YB,Liu, JW. Least-squares solution of inverse problem for hermitian anti-reflexive matrices and its appoximation[J]. ACTA MATHEMATICA SINICA-ENGLISH SERIES,2006,22(2):477-484.
APA	Peng, ZY,Deng, YB,&Liu, JW.(2006).Least-squares solution of inverse problem for hermitian anti-reflexive matrices and its appoximation.ACTA MATHEMATICA SINICA-ENGLISH SERIES,22(2),477-484.
MLA	Peng, ZY,et al."Least-squares solution of inverse problem for hermitian anti-reflexive matrices and its appoximation".ACTA MATHEMATICA SINICA-ENGLISH SERIES 22.2(2006):477-484.