基于凸优函数的Newton类方法的收敛定理

本文研究了求解Banach空间上非线性算子方程f(x)=0的Newton类方法的收敛性.利用优函数原理,在A(x0)1f满足关于某一凸优函数的广义Lipschitz条件下,得到了Newton类方法的一个半局部收敛定理.同时,当f和A(x)及初始点x0给定时,针对广义Lipschitz条件构造了相应的优函数,推广了Newton类方法的相关结果.

THE CONVERGENCE THEOREM OF THE NEWTON-LIKE METHODS BASED ON CONVEX MAJORANTS

In this paper,we study the convergence behaviour of Newton-like methods for solving the nonlinear operator equation f(x)=0 in a Banach space.By using majorants principle,when A(x 0) 1 f satisfies the generalized Lipschitz condition about some convex majorants,we derive the semilocal convergence theorem of Newton-like methods,and construct the majorant according to generalized Lipschitz condition when f and A(x) together with an initial guess x 0 are given.Then some results of Newton-like methods are general...