• 论文 •

### 有约束广义线性最小二乘拟合问题的求解方法

1. 中国船舶科学研究中心
• 出版日期:1981-02-20 发布日期:1981-02-20

### A METHOD FOR SOLVING GENERALIZED LINEAR LEAST SQUARES TO FIT PROBLEM WITH CONSTRAINTS

1. Zhou Lian-di China Ship Scientific Research Center
• Online:1981-02-20 Published:1981-02-20

In this paper, a method is given for solving the constrained linear least squares to fitproblem when the independent and dependent variables are both subject to error. Byusing Lagrangian Multiplier Method and Newton-Raphson Method for the solution of thenonlinear equation systems, the problem under an approximate assumpution can be reduc-ed by the iterative procedure between the constrained linear least squares to fit problemwith the independent variables without error and the suitable modification of the me-asured data of the independent variables.
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 [1] W. E. Deming, Statistical Adjustment of Data, New York, Wiley, 1943． [2] M. O'Neill, I. G. Sinclair, F. J. Smith, Computer Journal, 12: 1(1969) . [3] D. R. Powell, J. R. Macdonald, Computer Journal, 15: 2(1972) . [4] W. H. Southwell, Computer Journal, 19: 1 (1976) . [5] 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,计算数学,3(1979) . [6] K.Pearson,Phil.Mag., 2(1901) , 559-572． [7] 南京大学数学系计算数学专业编,最优化方法,科学出版社,1978．
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