非线性不适定问题一种双循环的牛顿型迭代格式

ON A NEWTON-TYPE METHOD FOR THE REGULARIZATION OF NONLINEAR ILL-POSED PROBLEMS

本文研究非线性算子方程F(x)=y的解,结合最速下降法,Newton-Landweber迭代格式及正则化思想,在F满足适当的条件下,构造出新的双循环迭代格式。本文对格式的收敛性进行了严格论证,并估计出迭代格式的收敛精度。

This paper considers a Newton-type method, for regularizing the abstract nonlinear ill-posed operator equation F(x) = y. Under certain smoothness conditions on the nonlinear operator, the authors obtain the local convergence of the method. By further assumptions on the closeness and smoothness of the exact solution, a stopping rule to terminate the iteration is proposed and the suitable rates of convergence is derived.