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.
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.
出处
《计算数学》
CSCD
北大核心
2005年第1期11-18,共8页
Mathematica Numerica Sinica
基金
中国博士后科学基金资助项目(2004035645).
