| 实矩阵反问题的总体最小二乘解及其最佳逼近 |
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| 引用本文： | 吕良福,徐欢,张加万.实矩阵反问题的总体最小二乘解及其最佳逼近[J].天津大学学报(自然科学与工程技术版),2009,42(5):453-457. |
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| 作者姓名： | 吕良福 徐欢 张加万 |
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| 作者单位： | 吕良福,LU Liang-fu(天津大学理学院,天津,300072);徐欢,XU Huan(天津市耀华中学数学组,天津,300040);张加万,ZHANG Jia-wan(天津大学计算机科学与技术学院,天津,300072)
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| 基金项目： | 国家自然科学基金，天津市自然科学基金 |
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| 摘 要： | 最小二乘法是近年来求解矩阵反问题的一种常用方法，但系数矩阵常常存在误差，方法本身具有很大局限性．鉴于此，提出并讨论了非对称矩阵反问题的总体最小二乘解，给出了解的一般表达式；证明了最佳逼近问题解的存在唯一性，给出了其具体表达式及数值算法，最后将数值结果用于求解非对称矩阵反问题．
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| 关 键 词： | 矩阵 反问题 总体最小二乘解 奇异值分解 |
Total Least-Squares Solution for Inverse Problems of Real Matrices and Its Optimal Approximation |
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| LU Liang-fu,XU Huan,ZHANG Jia-wan.Total Least-Squares Solution for Inverse Problems of Real Matrices and Its Optimal Approximation[J].Journal of Tianjin University(Science and Technology),2009,42(5):453-457. |
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| Authors: | LU Liang-fu XU Huan ZHANG Jia-wan |
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| Institution: | LU Liang-fu, XU Huan, ZHANG Jia-wan (1. School of Sciences,Tianjin University, Tianjin 300072,China 2. Maths Office,Yaohua High School,Tianjin 300040, China; 3. School of Computer Science and Technology, Tianjin University,Tianjin 300072 ,China) |
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| Abstract: | Least squares have been widely used in the inverse problems of matrices in recent years. However,errors fre- quently occur in the coefficient matrix, making the approach being limited in itself. In order to improve the limitation,the total least-squares solution of inverse problems was proposed. The general form of solution for the non-symmetric matrix was given,the expression of optimal approximation solution presented,the existence and unique of solution proved,and a numerical algorithm described. These results were applied in solving the inverse problems of non-symmetric matrices. |
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| Keywords: | matrix inverse problem total least-squares solution singular value decomposition |
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