关于高斯牛顿法的注记

Note about Gauss Newton Method

用牛顿法解最小二乘问题的主要困难是Hesse矩阵和二阶项的计算.文中研究可用已求得的一阶项代替二阶项的牛顿法.为此引入一个降阶条件,并讨论此条件下的牛顿法的性质,证明了此算法在适当条件下的收敛速度是二阶的,进而还能是超线性的.

The main difficulties of Least square problem with Newton＇s method is Hesse matrix and the calculation of the second order items. In this paper, the first order of available obtained instead of the second order term of Newton＇s method are studied . Therefore, a reduced order condition is introduced, and the nature of the Newton＇s method is discussed. The convergence of this algorithm is proved to the second order and the superlinear under the condition.