| 加权总体最小二乘问题的分析 |
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| 引用本文： | 魏木生,陈果良. 加权总体最小二乘问题的分析[J]. 计算数学, 1993, 15(1): 69-76 |
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| 作者姓名： | 魏木生 陈果良 |
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| 作者单位： | 华东师大数学系(魏木生)，华东师大数学系(陈果良) |
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| 摘 要： | 总体最小二乘问题由Golub和Van Loan首先进行数学的分析,随后人们对于总体最小二乘问题的算法、解的各种形式、总体最小二乘解和最小二乘解的关系、总体最小二乘解的扰动理论以及数值试验作了大量的研究工作。近来,[10]中给出了总体最小二乘问题(TLS)较一般地讨论。另一方面,Golub和Van Loan研究了总体最小二乘问题的特殊均加权形式。本文试图在[10,11]的基础上讨论最一般的总体最小二
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| 关 键 词： | 最小二乘法 总体最小二乘 |
AN ANALYSIS FOR THE WEIGHTED TOTAL LEAST SQUARES PROBLEM |
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| Affiliation: | Wei Mu-sheng;Chen Guo-liang Department of Mathematics, East China Normal University |
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| Abstract: | This paper presents an analysis of the weighted total least squares problem(WTLS). General formulas for the minimum norm WTLS solutions are given; fiveequivalent formulas for the solution set of the WTLS problem are proved; the er-ror bounds for the perturbed WTLS solutions are deduced. The analysis is usefulespecially for rank defficient problems and generalizes the results of Golub and VanLoan, Van Huffel and Vandewalle, and Wei. Numerical results for a practical application are also given to verify the error bounds. |
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