| 矩阵方程AXB＋CYD=E的中心对称解的递推算法 |
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| 引用本文： | 王伟,刘莉.矩阵方程AXB＋CYD=E的中心对称解的递推算法[J].宁夏师范学院学报,2010,31(3):5-9,35. |
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| 作者姓名： | 王伟 刘莉 |
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| 作者单位： | 宁夏大学,数学计算机学院,宁夏,银川,750021 |
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| 摘 要： | 讨论了矩阵方程AXB＋CYD=E中心对称解的迭代算法，该算法能够判断矩阵方程是否有中心对称解，在有解的条件下，能得到它的中心对称解，而且在选取特殊的初始矩阵时，该算法能够求出矩阵方程的极小范数中心对称解，以及对给定的矩阵进行最佳逼近的中心对称解．
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| 关 键 词： | 中心对称解 极小范数解 最佳逼近解 |
An Iterative Algorithm for the Centrosymmetric Solution of a Matrix Equation AXB+CYD=E |
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| WANG Wei,LIU Li.An Iterative Algorithm for the Centrosymmetric Solution of a Matrix Equation AXB+CYD=E[J].Journal of Ningxia Teachers College,2010,31(3):5-9,35. |
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| Authors: | WANG Wei LIU Li |
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| Institution: | WANG Wei,LIU Li(School of Mathematics and Computer Science,Ningxia University,Yinchuan,Ningxia 750021) |
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| Abstract: | The iterative method for the centrosymmetic solution of a matrix equation is presented,which can judge whether a linear matrix equation has the centrosymmetric solution.When the matrix equation has centrosymmetric solution pair,then for an in-itial matrix pair,centrosymmetric solution can be obtained within finite iterative steps in the absence of roundoff errors,and mini-mum norm of the centrosymmetric solution can be obtained by choosing a special kind of initial pair matrices.In addition,the u-nique opti... |
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| Keywords: | Centrosymmetric solution Least norm solution Optimal approximation solution |
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