Solving linearly constrained matrix least squares problem by LSQR

Matrix iterative algorithm LSQR is proposed for solving the linearly constrained matrix least squares (LS) problem. With the special properties of constraint matrix, Kronecker product and the coordinate mapping from the constrained space to its (independent) parameter space, we transform the constrained matrix LS problem to the unconstrained long vector least squares problem and rewrite the corresponding vector-form algorithm back to the matrix one. The resulting matrix-form iteration only consists of matrix–matrix product and does not involve the Kronecker product. Numerical results are reported to show the feasibility of the proposed method.