On the best approximate (P,Q)-orthogonal symmetric and skew-symmetric solution of the matrix equation AXB=C

Abstract

Suppose that the matrix equation AXB-C with unknown matrix X is given, where A, B, and C are known matrices of suitable size. The matrix nearness problem is considered over the (P, Q)-orthogonal symmetric and (P, Q)-orthogonal skew-symmetric solutions of the matrix equation AXB=C. The explicit forms of the best approximate solutions of the problems considered are established. Moreover, two numerical examples and a comparative table, depending on the examples chosen from literature, are given.