求解不可导算子的迭代法及其收敛性分析

Iteration for solving non-differentiable operator and the analysis for its convergence

主要研究了非线性算子不可导情形下Newton迭代型的收敛性.通过将不可导算子F分解为可导部分H和不可导部分G,借助Hernndez采用的修正迭代公式,分析了Newton型迭代的收敛性.相比Hernández的结果,本定理所需条件较弱,并且具有较好的误差估计公式.

Convergence of Newton-like iteration for the non-differentiable operator is considered. Dividing the non- differentiable operator F into two parts： the differentiable part H and the non-differentiable part G, making use of the modified iteration formula used by Hernandez, the convergence of the iteration is analyzed. Compared with the result of Hernandez＇s, the theorem needs milder condition and draw the better conclusion for error estimate.