Least Squares Solution of Matrix Equation AXB* + CYD* = E

We present an efficient algorithm for the least squares solution (X, Y) of the matrix equation AXB* + CYD* = E with arbitrary coefficient matrices A, B, C, D and the right-hand side E. This method determines the least squares solution (X, Y) with the least norm. It relies on the SVD and generalized SVD of the coefficient matrices and has complexity proportional to the cost of these SVDs.