仿射反变条件下Newton迭代法的半局部收敛性

摘要

The semi-local convergence properties of Newton's iteration method for nonlinear operator equations were studied under the hypothesis that the first derivative satisfies affine contravariant ω-condition.This condition includes the affine contravariant Lipschitz condition and the affine contravariant H(o)lder condition as special cases.Moreover, the estimations of the iterative residual ( ‖ F(xκ) ‖ ) were given and the results obtained before were extended.%研究了一阶导数满足仿射反变ω-条件下,Newton迭代法在求解非线性算子方程时的半局部收敛性.这种ω-条件包含了仿射反变Lipschitz条件和仿射反变H(O)lder条件作为特殊情形.此外,得到了相应迭代残余(‖F(xk)‖)的误差估计,并推广了相应结果.