THE INVERSE PROBLEM FOR PART SYMMETRIC MATRICES ON A SUBSPACE

• 来源期刊: 计算数学（英文版）
• 学科: 数学
• 关键词: Part symmetric matrix Inverse problem Optimal approximation.
• 年，卷（期）: 2003,（4）
• 页码范围: 505-512
• 页数: 8页
• 分类号: O24
• 语种: 英文

摘要

In this paper, the following two problems are considered:Problem I. Given S ∈ Rn×p, X, B ∈ Rn×m, find A ∈ SRs,n such that AX = B, where SRs,n = {A ∈ Rn×n|xT(A - AT) = 0, for all x ∈ R(S)}.Problem Ⅱ. Given A* ∈ Rn×n, find A ∈ SE such that ‖A^-A*‖ = minA∈sE‖A-A*‖,where SE is the solution set of Problem Ⅰ.The necessary and sufficient conditions for the solvability of and the general form of the solutions of problem Ⅰ are given. For problem Ⅱ, the expression for the solution, a numerical algorithm and a numerical example are provided.