| 求矩阵方程AXB+CXD=F的中心对称最小二乘解的迭代算法 |
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| 引用本文： | 尚丽娜,张凯院.求矩阵方程AXB+CXD=F的中心对称最小二乘解的迭代算法[J].数学物理学报(A辑),2010,30(3):776-783. |
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| 作者姓名： | 尚丽娜 张凯院 |
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| 作者单位： | 尚丽娜(西北工业大学应用数学系,西安710072;中国飞行试验研究院测试所,西安710089);张凯院(西北工业大学应用数学系,西安,710072) |
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| 摘 要： | 该文建立了求矩阵方程AXB+CXD=F的中心对称最小二乘解的迭代算法.使用该算法不仅可以判断该矩阵方程的中心对称解的存在性,而且无论中心对称解是否存在,都能够在有限步迭代计算之后得到中心对称最小二乘解.选取特殊的初始矩阵时,可求得极小范数中心对称最小二乘解.同时,也能给出指定矩阵的最佳逼近中心对称矩阵.
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| 关 键 词： | 矩阵方程 中心对称矩阵 最小二乘解 极小范数解 迭代算法 最佳逼近 |
| 收稿时间： | 2007-12-12 |
| 修稿时间： | 2009-08-30 |
An Iterative Method for the Least Squares Centrosymmetric Solution of the Matrix Equation AXB+CXD=F |
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| SHANG Li-Na,ZHANG Kai-Yuan.An Iterative Method for the Least Squares Centrosymmetric Solution of the Matrix Equation AXB+CXD=F[J].Acta Mathematica Scientia,2010,30(3):776-783. |
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| Authors: | SHANG Li-Na ZHANG Kai-Yuan |
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| Institution: | 1. Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072|2. Department of Test, Chinese Flight Test Establishment, Xi'an 710089 |
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| Abstract: | An iterative method is presented to solve the minimum Frobenius norm residual problem: min AXB+CXD-F with unknown centrosymmetric matrix X. By this iterative method, for any initial centrosymmetric matrix X0, a solution X* can be obtained automatically within finite iteration steps in the absence of roundoff errors, and the solution X* with least Frobenius norm can be obtained by choosing a special initial centrosymmetric matrix. In addition, its optimal approximation matrix to a given matrix can be obtained. Numerical examples are given to show that the intertive method is quite efficient. |
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| Keywords: | Matrix equationzz Centrosymmetric matrixzz Least squares solutionzz Least-norm solutionzz Iterative methodzz Optimal approximationzz |
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