摘要
本文借助于正则化理论,通过添加稳定泛函μΩ(z)=μ2‖xk-xk-1‖2,结合修正高斯-牛顿法,构造了非线性最小二乘问题正则化修正高斯-牛顿法求解公式;解决了普通修正高斯-牛顿法在迭代过程中其Jacobian矩阵是秩亏或者严重病态导致的不能收敛的问题;给出了非线性秩亏自由网平差的正则化修正高斯-牛顿法步骤;最后以几个经典非线性最小二乘问题为例进行了数值实验,说明了本文所提方法的正确性和适用性。
Based on regularization theory, by adding the stable function μΩ（z）=μ^2‖xk-xk-1‖^2 and referring to the modified Gauss-Newton method, this paper constructs the regularization modified Gauss-Newton method to solve the nonlinear least square problem. The method could solve the problems that lead to non-convergence because of the rank-deficient Jacobian matrix or very ill-conditioned in numerical iterative process. This paper not only gives the procedure of the constructed method for solving NLS problem, but also puts forward the approach of solving nonlinear adjustment of free networks with rank deficiency. The numerical experiment shows that the method mentioned here is accurate and useful.
出处
《工程勘察》
CSCD
北大核心
2009年第6期58-61,共4页
Geotechnical Investigation & Surveying
基金
湖南省科技计划项目(2008SK3054)
关键词
NLS问题
正则化
修正高斯-牛顿法
数值迭代
不适定问题
nonlinear least square problem
regularization
modified Gauss-Newton method
numerical iterative
III-posed problems
