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有约束广义线性最小二乘拟合问题的求解方法

周连第   

  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

周连第. 有约束广义线性最小二乘拟合问题的求解方法[J]. 数值计算与计算机应用, 1981, 2(2): 98-104.

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
实验数据的最小二乘拟合问题,已经在各个领域中得到广泛的应用,并且已经发展了许多富有成效的数值计算方法.但是在许多实验情况下,不但自变量x和因变量y都不可避免地带有误差,而且自变量x的误差大于通常可以忽略的情况.此时通常的最小二乘拟合方法就不适用了.自变量和因变量都具有误差的最小二乘拟合问题,称为广义最小
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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[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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