| 关于TLS问题 |
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| 引用本文： | 魏木生,朱超.关于TLS问题[J].计算数学,2002,24(3):345-352. |
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| 作者姓名： | 魏木生 朱超 |
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| 作者单位： | 华东师范大学数学系,上海,200062 |
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| 基金项目： | 国家自然科学基金（No.19871029），上海市重点学科建设基金和国家高性能计算中心资助项目. |
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| 摘 要： | 1.引 言考虑观测线性系统AX=B,（1.1a）其中A∈Cm×n,B∈Cm×d（本文通篇假设m≥n d）,分别是精确但不可观测的A0∈Cm×n,B0∈Cm×d的近似,即精确线性系统是A0X=B0.（1.1b）Golub和Van Loan于1980年提出的总体最小二乘问题（以下简称TLS问题）就是求解线性系统AX=B（1.2）
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| 关 键 词： | TLS问题 总体最小二乘 奇异值分解 修正矩阵 线性系统 解 |
| 修稿时间： | 2001年4月27日 |
ON THE TOTAL LEAST SQUARES PROBLEM |
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| Wei Musheng Zhu Chao.ON THE TOTAL LEAST SQUARES PROBLEM[J].Mathematica Numerica Sinica,2002,24(3):345-352. |
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| Authors: | Wei Musheng Zhu Chao |
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| Institution: | Wei Musheng Zhu Chao (Department of Mathematics, East China Normal University, Shanghai, 200062) |
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| Abstract: | The total least squares(TLS) is a method of solving an overdetermined system of linear equations AX = B that is appropriate when there are errors in both A and B. Golub and Van Loan(G. H. Golub and C. F. Van Loan, SIAM J. Numer. Anal. 17(1980), 883-893) introduced this method into the field of numerical analysis and developed an algorithm based on singular value decomposition. While M. Wei(M. Wei, Numer. Math. 62(1992), 123-148) proposed a new definition for TLS problem. In this paper, we discuss the relations between the two definitions. As a result, one can see that the latter definition is a generalization of the former one. |
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| Keywords: | Total least squares Singular value decomposition Correction matrix |
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