Iterative method for the least squares problem of a matrix equation with tridiagonal matrix constraint

The matrix-form LSQR method is presented in this paper for solving the least squares problem of the matrix equation AXB = C with tridiagonal matrix constraint. Based on a matrix-form bidiagonalization procedure, the least squares problem associated with the tridiagonal constrained matrix equation AXB = C reduces to a unconstrained least squares problem of linear system, which can be solved by using the classical LSQR algorithm. Furthermore, the preconditioned matrix-form LSQR method is adopted for solving the corresponding least squares problem.