| 矩阵方程AX=B的双反对称最佳逼近解 |
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| 引用本文： | 张新东,张知难.矩阵方程AX=B的双反对称最佳逼近解[J].应用数学学报,2009,32(5). |
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| 作者姓名： | 张新东 张知难 |
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| 作者单位： | 1. 新疆师范大学数理信息学院,乌鲁木齐,830054
2. 新疆大学数学与系统科学学院,乌鲁木齐,830046 |
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| 基金项目： | 新疆师范大学博士科研启动基金 |
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| 摘 要： | 本文主要讨论下而两个问题并得到相关结果:问题Ⅰ:给定A ∈ R~(k×n),B ∈ R~(k×n),求X ∈ BASR~(n×n),使得AX=B.问题Ⅱ:给定X* ∈R~(n×n),求X使得‖X-X~*‖=minX∈S_E‖X-X~*‖,其中S_E是问题Ⅰ的解集合,‖·‖是Frobenius范数.通过对上述问题的讨论给出了问题Ⅰ解存在的充分必要条件和其解的一般表达式同时给出了问题Ⅱ的解,算法,和数值例子.
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| 关 键 词： | 双反对称矩阵 反对称矩阵 Frobenius范数 最佳逼近 |
The Anti-bisymmetric Matrices Optimal Approximation Solution of Matrix Equation AX = B |
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| ZHANG XINDONG,ZHANG ZHINAN.The Anti-bisymmetric Matrices Optimal Approximation Solution of Matrix Equation AX = B[J].Acta Mathematicae Applicatae Sinica,2009,32(5). |
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| Authors: | ZHANG XINDONG ZHANG ZHINAN |
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| Abstract: | This paper is mainly concerned with solving the following two problems,Problem Ⅰ: Given k × n real matrices A and B, find X ∈ BASR~(n×n) such that AX = B.Problem Ⅱ: Given an ~(n×n) real matrix X~*, find an n×n matrix X such that ‖X-X~*‖=X ∈S_E‖X-X~*‖,wher‖·‖is a Frobenius norm,and S_E is the solution set of Problem Ⅰ.The necessary and sufficient conditions for the existence and expressions of the gen-eral solutions of Problem Ⅰ are given. The explicit solution, a numerical algorithm and a numerical example to Problem Ⅱ are provided. |
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| Keywords: | anti-bisymmetric matrix anti-symmetric matrix frobenius norm optimal approximation |
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