Matrix iterative solutions to the least squares problem of BXATÂ =Â F with some linear constraints

Matrix iterative algorithms are proposed for solving the matrix least square problem of BXAT = F with variant linear constraints on solutions such as symmetry, skew-symmetry, and symmetry/skew-symmetry commuting with a given symmetric matrix P. We characterize the linear mapping from the constrained solution sets to their (independent) parameter spaces, and use these properties to deduce the matrix iterations, based on the classical algorithm LSQR for solving (unconstrained) LS problem. Numerical results are reported that show the efficiency of the proposed methods.