| 线性子空间上求解AX=B的最小二乘问题的迭代算法 |
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| 引用本文： | 周海林.线性子空间上求解AX=B的最小二乘问题的迭代算法[J].计算数学,2023,45(1):93-108. |
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| 作者姓名： | 周海林 |
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| 作者单位： | 南京理工大学泰州科技学院, 泰州 225300 |
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| 基金项目： | 江苏高校“青蓝工程”(2020)资助项目. |
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| 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.
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| 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 |
| 收稿时间： | 2021-07-07 |
AN ITERATIVE ALGORITHM TO THE LEAST SQUARES PROBLEM OF AX=B OVER LINEAR SUBSPACE |
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| Zhou Hailin.AN ITERATIVE ALGORITHM TO THE LEAST SQUARES PROBLEM OF AX=B OVER LINEAR SUBSPACE[J].Mathematica Numerica Sinica,2023,45(1):93-108. |
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| Authors: | Zhou Hailin |
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| Institution: | Taizhou Institute of Sci. & Tech., NJUST., Taizhou 225300, China |
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| Abstract: | 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. |
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| Keywords: | linear subspace conjugate gradient projection operator least squares solution optimal approximation |
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