计算数学 2005, 27(1) 11-18 DOI:     ISSN: 0254-7791 CN: 11-2125/O1

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PubMed

双对称矩阵的一类反问题

彭振赟,胡锡炎,张磊

湖南科技大学数学系,湖南大学应用数学系,湖南大学应用数学系 湘潭,411201 中南大学数学系,长沙,410083 ,长沙,410082 ,长沙,410082

摘要

给定矩阵X和B,得到了矩阵方程XTAX=B有双对称解的充分必要条件及有解时解的一般表达式.用SE表示此矩阵方程的解集合,证明了SE中存在唯一的矩阵A,使得A与给定矩阵A*的差的Frbenius范数最小,并且给出了矩阵A的表达式.

关键词

ONE KIND OF INVERSE PROBLEM FOR THE BISYMMETRIC MATRICES

Peng Zhenyun(Department of Mathematics, Hunan University of Science and Technology, Xiangtan, 411201; Department of Mathematics, Central South University, Changsha 410083)Hu Xiyan Zhang Lei (Department of Applied Mathematics, Hunan University, Changsha 410082)

Abstract:

In this paper, we first consider the solution of the matrix equation as follow: Find a bisymmetric matrix such that for given matrices X, B we have XTAX = B. The necessary and sufficient conditions for the existence of and the expressions for the solutions of the matrix equation are obtained. We denote the set of such solutions by SE. Then the matrix nearness problem for the matrix equation is discussed. That is: Given an arbitrary A*, find a matrix A ∈ SE which is nearest to A* in Probenius norm. We show that the nearest matrix is unique and provide an expression for this nearest matrix.

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收稿日期  修回日期  网络版发布日期 2005-01-14 00:00:00.0 
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