ON THE MATRIX NEARNESS PROBLEM FOR (SKEW-)SYMMETRIC MATRICES ASSOCIATED WITH THE MATRIX EQUATIONS (A(1)XB(1),..., A(k)XB(k)) = (C-1,...,C-k)

Abstract

Suppose that the matrix equations system (A(1)XB(1), ... , A(k)XB(k)) = (C-1,..., C-k) with unknown matrix X is given, where A(i), B-i, and C-i, i = 1, 2,..., k, are known matrices of suitable sizes. The matrix nearness problem is considered over the general and least squares solutions of this system. The explicit forms of the best approximate solutions of the problems over the sets of symmetric and skew-symmetric matrices are established as well. Moreover, a comparative table depending on some numerical examples in the literature is given.