| 一类不相容矩阵方程对最小Frobenius范数问题的迭代算法(英) |
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| 引用本文： | 徐相建,王明辉,魏木生.一类不相容矩阵方程对最小Frobenius范数问题的迭代算法(英)[J].华东师范大学学报(自然科学版),2008,2008(3):30-36. |
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| 作者姓名： | 徐相建 王明辉 魏木生 |
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| 作者单位： | [1]南通大学理学院,江苏南通226007 [2]华东师范大学数学系,上海200062 |
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| 摘 要： | 提出了关于不相容矩阵方程对(AXB,CXD)=(E,F)最小Frobenius范数问题的一个迭代算法. 对于任意的初始矩阵X0, 在没有舍入误差的情况下, 运用此算法能在有限步内得到方程对在Frobienius范数意义下的最小解. 数值例子表明提出算法的有效性.
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| 关 键 词： | 迭代算法 Kronecker积 矩阵方程对 迭代算法 Kronecker积 矩阵方程对 |
| 收稿时间： | 2007-6-25 |
| 修稿时间： | 2007-9-17 |
Iterative algorithm for solving least Frobenius norm problem of an inconsistent matrix equation pair(English) |
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| XU Xiang-jian,WANG Ming-hui,WEI Mu-sheng.Iterative algorithm for solving least Frobenius norm problem of an inconsistent matrix equation pair(English)[J].Journal of East China Normal University(Natural Science),2008,2008(3):30-36. |
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| Authors: | XU Xiang-jian WANG Ming-hui WEI Mu-sheng |
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| Institution: | 1. School of Science, Nantong University, Nantong Jiangsu 226007, China
2. Department of Mathematics, East China Normal University, Shanghai 2000621, China |
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| Abstract: | This paper presented an iterative algorithm for solving the least Frobenius norm problem of inconsistent matrix equation pair (AXB,CXD)=(E,F) with a real matrix X. By this algorithm, for any (special) initial matrix X0, a solution (the minimal Frobienius norm solution) can be obtained within finite iteration steps in the absence of roundoff errors. The numerical examples verify the efficiency of the algorithm. |
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| Keywords: | iterative algorithm Kronceker product matrix equation pair |
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