(untitled) (Journal of Computational Mathematics, 2003)
In this paper, the following two problems are considered: Problem Ⅰ. Given S R^n×p, X, B R^n×m, find A SR_s,n such that AX=B, where SR_s,n=A R^n×n | x^T(A-A^T)=0, for all x R(S). Problem Ⅱ. Given A^* R^n×n, find A S_E such that \|A -A^*\|=min_A S_E \|A-A*\|, where S_E is the solution set of Problem Ⅰ. Then necessary and sufficient conditions for the solvability of and the general from 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.