基于凸优函数的Newton类方法的收敛定理

摘要

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(x0)-1f1 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 x0 are given. Then some results of Newton-like methods are generalized.%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.