线性子空间上求解AX=B的最小二乘问题的迭代算法

AN ITERATIVE ALGORITHM TO THE LEAST SQUARES PROBLEM OF AX=B OVER LINEAR SUBSPACE

应用共轭梯度方法和线性投影算子,给出迭代算法求解了线性矩阵方程AX=B在任意线性子空间上的最小二乘解问题.在不考虑舍入误差的情况下,可以证明,所给迭代算法经过有限步迭代可得到矩阵方程AX=B的最小二乘解、极小范数最小二乘解及其最佳逼近.文中的数值例子证实了该算法的有效性.

Applying the conjugate gradient method and linear projection operator,an iterative algorithm is presented to solve the least squares problem of linear matrix equation AX=B over any linear subspace.It is proved that the least squares solution,the minimum-norm least squares solution and the optimal approximation of the matrix equation AX=B can be obtained in finite iteration steps by the method without considering rounding errors.The numerical examples verify the efficiency of the algorithm.