关于简化Newton方法收敛性的注记

A note on the convergence of the simplified Newton's method

在假设算子方程解存在的前提下,给出了以解为中心的一个球域,证明了当初始点落到这个球域时,用于判断简化Newton方法收敛性的Kantorovich定理的条件必然满足,从而由简化Newton方法产生的迭代序列收敛.

Under the supposition that there exists a solution for nonlinear operator equations, a ball with this solution as its center is given. We prove that only if initial point of the simplified Newton＇s method lies in this ball, all the conditions of the Kantorovich theorem for this method are satisfied, and the iteration sequence generated by this method converges.