THE SOLVABILITY CONDITIONS FOR THE INVERSE PROBLEM OF BISYMMETRIC NONNEGATIVE DEFINITE MATRICES

• 来源期刊: 计算数学（英文版）
• 关键词: Frobenius norm Bisymmetric matrix The optimal solution.
• 年，卷（期）: 2000,（6）
• 页码范围: 597-608
• 页数: 12页
• 语种: 英文

摘要

A = (aij) ∈ Rn×n is termed bisymmetric matrix if aij = aji = an-j+1,n-i+1, i,j = 1,2...n. We denote the set of all n × n bisymmetric matrices by BSRn×n. This paper is mainly concerned with solving the following two problems: Problem I. Given X, B ∈ Rn×m, find A ∈ Pn such that AX = B, where Pn = {A ∈ BSRn×n] xTAx ＜ 0, Ax ∈ Rn}. Problem II. Given A* ∈ Rn×n, find A ∈ SE such that where ‖ ·‖F is Frobenius norm, and SE denotes the solution set of problem I. The necessary and sufficient conditions for the solvability of problem I have been studied. The general form of SE has been given. For problem II the expression of the solution has been provided.