线性子空间上求解AXB=C的最小二乘解的迭代算法
AN ITERATIVE ALGORITHM TO THE LEAST SQUARES SOLUTION OF AXB=C OVER LINEAR SUBSPACE
周海林1
作者信息
- 1. 南京理工大学泰州科技学院,泰州 225300
- 折叠
摘要
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AXB=C在任意线性子空间上的最小二乘解.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AXB=C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.本文算法的优点是在任意线性子空间上均容易实现.
Abstract
Applying the conjugate gradient method and linear projection operator,an iterative algorithm is presented to solve the least squares solution of linear matrix equation AXB=C under 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=C can be obtained in finite iteration steps by the method without considering rounding errors.The numerical examples verify the efficiency of the algorithm.The merit of our method is that it is easy to implement in any linear subspace.
关键词
线性子空间/共轭梯度/投影算子/最小二乘解/最佳逼近Key words
Linear subspace/Conjugate gradient/Projection operator/Least squares solution/Optimal approximation引用本文复制引用
出版年
2024
NETL
NSTL
万方数据