Least-Squares Solutions of the Matrix Equations AXB+CYD=H and AXB+CXD=H for Symmetric Arrowhead Matrices and Associated Approximation Problems

Abstract

The least-squares solutions of the matrix equations $AXB+CYD=H$ and $AXB+CXD=H$ for symmetric arrowhead matrices are discussed. By using the Kronecker product and stretching function of matrices, the explicit representations of the general solution are given. Also, it is shown that the best approximation solution is unique and an explicit expression of the solution is derived.