子空间约束下矩阵方程A^TXB+B^TX^TA=D的解及最佳逼近

THE SOLUTION AND OPTIMAL APPROXIMATION OF MATRIX EQUATION A^TXB+B^TX^TA=D UNDER SUBSPACE CONSTRAINT

约束矩阵方程求解是指在满足一定约束条件下求矩阵方程(组)的解.在子空间约束条件下,利用共轭梯度法,结合线性投影算子,得到矩阵方程A^TXB+B^TX^TA=D的解,进一步得到其最佳逼近.最后用数值例子证实了算法的有效性.

Solving the constrained matrix equation problem refers to finding the solution of the matrix equation(group)under certain constraint conditions.Under the constraint of subspace,by conjugate gradient method and linear projection operator,the solution of matrix equation A^TXB+B^TX^TA=D and its optimal approximation are obtained.Finally,numerical examples are further used to verify the effectiveness of the algorithm.