摘要
1.引言
近几年来,对矩阵反问题AX=B的研究已取得了许多进展[1,2].最近,胡锡炎等[3]研究了对称正交对称矩阵反问题,给出了问题有解的条件.但在结构模型修正等实际问题中,矩阵X和B通常由试验给出,一般难以保证问题的解存在.因此本文讨论对称正交对称矩阵反问题的最小二乘解.
Let P ∈ Rn×n be a symmetric orthogonal matrix. A∈Rn×n is called a symmetric orthogonal symmetric matrix if AT = A and (PA) T = PA. The set of all n × n symmetric orthogonal symmetric matrices is denoted by SRnxnp. This paper discusses the following problems: Problem I. Given X,B∈ Rn×m, find A ∈SRn×np such that||AX - B|| = min Problem II. Given A∈ Rn×n, find A∈SL such thatwhere ||·|| is the Frobenius norm, and SL is the solution set of Problem I.The general form of SL is given. The solvability conditions for the inverseproblem AX = B in SRn×nP are obtained. The expression of the solution toProblem II is presented.
出处
《计算数学》
CSCD
北大核心
2003年第1期59-66,共8页
Mathematica Numerica Sinica
基金
国家自然科学基金(10271055)
江苏省"青蓝工程"基金资助项目
