An Iterative Method for Different Constrained Least Square Solution of a Multi-Variables Linear Matrix Equation

摘要

An iterative method is constructed to find the different constrained least square solution by constructing the equivalent linear matrix equations, and revising the drop direction of the conjugate gradient method and its related coefficient, and its convergence is proved. By this iterative method, the different constrained least square solution can be obtained within finite iterative steps in the absence of round off errors, and the different constrained least square solution with least-norm can be got by choosing special initial matrix. In addition, the optimal approximation matrix to any given matrix can be obtained in the set of the different constrained least square solutions. The numerical examples show that the iterative method is efficient.