| 矩阵方程组A1XB1+C1XD1=F1,A2XB2+C1XD2=F2的反对称解及其最佳逼近 |
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| 引用本文： | 梁开福,王贵初.矩阵方程组A1XB1+C1XD1=F1,A2XB2+C1XD2=F2的反对称解及其最佳逼近[J].湘潭大学自然科学学报,2011,33(3). |
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| 作者姓名： | 梁开福 王贵初 |
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| 作者单位： | 湘潭大学数学与计算科学学院,湖南湘潭,411105 |
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| 基金项目： | 湖南省自然科学基金项目 |
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| 摘 要： | 利用迭代方法来解线性矩阵方程组A1XB1 +C1XD1 =F1,A2XB2+ C2XD2=F2.若这个矩阵方程组是相容的,那么它的反对称解就能在有限步迭代中得到.如果选取一个特殊的初始矩阵,就能够求得其最小范数解.若任意给定一个矩阵,可在A1(X-)B1 +C1 (X-)D1=F1,A2(X-)B2+C2(X-)D2 =F2中求得它的最佳逼近解.最后通过实例说明了这种迭代算法是有效的.
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| 关 键 词： | 迭代方法 反对称解 最小范数解 最佳逼近解 |
The Anti-Symmetric Solution and Optimum Appromation of the Matrix Equations A1XB1 +C1XD1 =F1 ,A2XB2 +C2XD2 =F2 |
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| LIANG Kai-fu,WANG Gui-chu.The Anti-Symmetric Solution and Optimum Appromation of the Matrix Equations A1XB1 +C1XD1 =F1 ,A2XB2 +C2XD2 =F2[J].Natural Science Journal of Xiangtan University,2011,33(3). |
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| Authors: | LIANG Kai-fu WANG Gui-chu |
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| Institution: | LIANG Kai-fu,WANG Gui-chu(School of Mathematics and Computational Science,Xiangtan University,Xiangtan 411105 China) |
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| Abstract: | In this paper,an iterative method is constructed to solve the linea matrix equations A1XB1+C1XD1=F1,A2XB2+C2XD2=F2.When this system of matrix equations is consistent,its solution can be obtained within finite iterative steps and its least-norm antisymmetric solution can be obtained by choosing a special kind of initial iterative matrix.Furthermore,its unique optimal approximation solution to a given matrix can be derived by finding the least-norm antisymmetric solution of a new system of matrix equations A1... |
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| Keywords: | iterative method antisymmetric solution least-norm antisymmetric solution optimal approximation |
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