Least squares solutions of the matrix equation AXB+CYD=E with the least norm for symmetric arrowhead matrices

摘要

In this paper, the least squares solution of the matrix equation AXB+CYD=E for symmetric arrowhead matrices with the least norm is discussed. By using Moore–Penrose inverse and the Kronecker product, the general expression of the solution to this problem is derived. A corresponding numerical algorithm and an example are also given.