关键词: 线性矩阵方程, 异类约束最小二乘解, 迭代算法, 极小范数解, 最佳逼近

Abstract:

The constrained solution to multivariable linear matrix equations has been widely used in parametre identification,structural design,vibration theory,automatic control theory and so on.Based on the iterative method for the same constrained least square solution of the linear matrix equation, an iterative method is constructed for different constrained least square solution of the linear matrix equation by constructing equivalent linear matrix equations. And the convergence of this method can be proved. By this method, a different constrained least square solution can be obtained within finite iterative steps in the absence of roundoff errors, and the different constrained least square solution with leastnorm can be obtained by choosing special initial matrices. In addition, the optimal approximation matrix to any given matrix can be obtained in the set of different constrained least square solutions. Examples show that the method is efficient.

Key words: linear matrix equation;different constraint least square solution;iterative method;leastnorm solution;optimal approximation