| 矩阵约束下的最佳逼近计算机算法 |
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| 引用本文： | 傅少川,徐成贤. 矩阵约束下的最佳逼近计算机算法[J]. 山东农业大学学报(自然科学版), 2009, 40(1) |
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| 作者姓名： | 傅少川 徐成贤 |
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| 作者单位： | 西安交通大学理学院,陕西,西安,710049;北京交通大学经管学院,北京,100044;西安交通大学理学院,陕西,西安,710049 |
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| 摘 要： | 本文首先研究矩阵方程约束下的两类最佳逼近问题,这两类问题是IELS问题、矩阵谱约束下最佳逼近问题和加权最小二乘问题等最佳逼近问题的一般形式.然后应用奇异值分解理论,根据最佳逼近的充要条件证明了第一类问题解的存在性及第二类问题解的唯一性,同时证明了这两类最佳逼近问题解的具体形式,最后给出了可用于计算机求解的解法步骤.
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| 关 键 词： | 矩阵函数 最佳逼近 特征值 计算机算法 |
COMPUTER SOLUTION OF BEST APPROXIMATION RESTRICTED BY MATRIX |
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| FU Shao-chuan,XU Cheng-xian. COMPUTER SOLUTION OF BEST APPROXIMATION RESTRICTED BY MATRIX[J]. Journal of Shandong Agricultural University, 2009, 40(1) |
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| Authors: | FU Shao-chuan XU Cheng-xian |
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| Affiliation: | 1.School of Science;Xi'an Jiaotong University;Xi'an 710049;China;2.School of Economic and Management;Beijing Jiaotong University;Beijing 100044;China |
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| Abstract: | This paper first research two problems of best approximation restricted by matrix,and this two problems are the generalization of the problem of IELS,best approximation restricted by matrix spectrum and weighted least squares estimate.Then the paper applies singular value decomposition(SVD)theory to prove the existence of the solution according to the necessary and sufficient conditions of the best approximation.At the end of this paper we provide a solution step that can be used in computer. |
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| Keywords: | Matrix function best approximation eigenvalue computer algorithms |
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