(untitled) (Journal of Computational Mathematics, 2021)
A = (a_ij) R^n×n is termed bisymmetric matrix if a_ij = a_ji = a_n-j+1,n-i+1, i,j=1,2, ..., n. We denote the set of all n × n bisymmetric matrices by BSR^n×n. This paper is mainly concerned with solving the following two problems: Problem I. Given X, B R^n×m, find A P_n such that AX=B, where P_n = { A BSR^n×n| x^TAx 0, x R^n }. Problem Ⅱ. Given A^* R^n×n, find A S_E such that \| A^* -A\|_F =min_A S_E \| A^* - A \|_F, where \|·\|_F is Frobenius norm, and S_E 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 S_E has been given. For problem II the expression of the solution has been provided.