On a general regularization scheme for nonlinear ill-posed problems
On a general regularization scheme for nonlinear ill-posed problems
复制标题
非线性不适定问题的一般正则化方案
DOI：
--
复制
发表时间：
1997
期刊：
影响因子：
--
通讯作者：
U. Tautenhahn
中科院分区：
文献类型：
--
作者：
U. Tautenhahn
本文引入一种广义正则化方案来重构非线性不适定问题F(x)=y的解，其中给出的不是y个噪声数据，而是Hilbert空间x和y之间的一个非线性算子。在该正则化方案中，正则化解定义为非线性方程的一个不动点，其中和表示。在给定非线性算子F和单元的光滑性的条件下，给出了稳定性估计，证明了在适当选择函数和正则化参数的情况下，正则化解的精度是阶最优的。
In this paper we introduce a general regularization scheme to reconstruct solutions of nonlinear ill-posed problems F(x)=y where instead of y noisy data with are given and is a nonlinear operator between Hilbert spaces X and Y. In this regularization scheme regularized solutions are defined as a fixed point of the nonlinear equation where and stands for . Assuming certain conditions concerning the nonlinear operator F and the smoothness of the element we derive stability estimates which show that the accuracy of the regularized solutions is order optimal provided that the function and the regularization parameter have been chosen properly.