| 关于用拉格朗日乘子法求解线性等式约束最小二乘问题 |
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| 引用本文： | 周连第.关于用拉格朗日乘子法求解线性等式约束最小二乘问题[J].计算数学,1979,1(3):264-271. |
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| 作者姓名： | 周连第 |
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| 作者单位： | 中国船舶科学研究中心 |
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| 摘 要： | 本文讨论用拉格朗日乘子法求解线性等式约束最小二乘问题(简称 LSE 问题)的优点.应用此法能细致地讨论约束条件与变量之间的关系,据此并可证明 LSE 问题与某一个无约束最小二乘问题的等价性.此外,尚可得到参数和拉格朗日乘子的协方差矩阵.最后给出一个数值稳定的解 LSE 问题的算法.
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ON THE PROCESS OF SOLVING THE LINEAR EQUALITY CONSTRAINED LEAST SQUARES PROBLEM BY LAGRANGIAN MULTIPLIER METHOD |
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| Institution: | Zhou Lian-di (China Ship Scientific Research Centre) |
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| Abstract: | In this paper the advantages of solving the linear equality constrained least squares problem (denoted by LSE Problem) by Lagrangian Multiplier Method are di- scussed.By this method,the relationship between the constrained conditions and the variables can be discussed in detail,and thus it can be demonstrated the existance of an unconstrained least squares problem which is equivalent to LSE problem.Fur- thermore,the convariance matrices of the parameters and the Lagrangian multipliers can be obtained.Finally,a numerically stable solution of LSE Problem is given. |
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