| 矩阵方程AXB=C的中心对称最小二乘解的迭代解法 |
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| 引用本文： | 张艳燕.矩阵方程AXB=C的中心对称最小二乘解的迭代解法[J].湖南文理学院学报(自然科学版),2009,21(2):8-11. |
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| 作者姓名： | 张艳燕 |
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| 作者单位： | 湖南文理学院,数学与计算科学学院,湖南,常德,415000
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| 基金项目： | 湖南文理学院院级一般项目 |
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| 摘 要： | 给出了求矩阵方程AXB=C的中心对称最小二乘解的一种迭代解法,即利用法方程变换,将求解最小二乘解转化为相容矩阵方程的求解问题,再利用迭代法求出新方程的直接解.使用该方法,对任意给定的初始中心对称矩阵都可在有限步内迭代求出它的中心对称最小二乘解.并且将求最佳逼近的问题转化为求一个新方程的极小范数解的问题,同样可用迭代法求解.
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| 关 键 词： | 迭代法 Frobenius范数 中心对称矩阵 最小二乘解 最佳逼近解 |
The iterative method for the centrosymmetric least-squares solutions and the optimal approximation to the matrix Eequation AXB = C |
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| ZHANG Yan-yan.The iterative method for the centrosymmetric least-squares solutions and the optimal approximation to the matrix Eequation AXB = C[J].Journal of Hunan University of Arts and Science:Natural Science Edition,2009,21(2):8-11. |
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| Authors: | ZHANG Yan-yan |
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| Institution: | Mathmatics and Computing Science College;Hunan University of Arts and Science;Changde;Hunan;415000 |
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| Abstract: | An iterative method was presented to solve the centrosymmetric least-squares solutions of the matrix equation AXB =C . By applying the orthogonal method of matrix equation, the problem of solving the least-squares solutions to the matrix equation to another problem of solving a consistent matrix equation. Then the direct centrosymmetric solutions were obtained by applying the iterative method in finite steps an arbitrary initializing centrosymmetric matrix. Also, the optimal approximated problem can be cove... |
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| Keywords: | iterative method Frobenius norm centrosymmetric matrix least-squares solution optimal approximation |
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