On the asymptotical regularization of nonlinear ill-posed problems
On the asymptotical regularization of nonlinear ill-posed problems
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DOI：
10.1088/0266-5611/10/6/014
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发表时间：
1994-12
期刊：
影响因子：
2.1
通讯作者：
U. Tautenhahn
中科院分区：
文献类型：
--
作者：
U. Tautenhahn
研究了求解非线性不适定问题F（x）=y的渐近正则化方法，其中用噪声数据y_（delta）=y代替y，且//y-y_（delta）//<或= delta，且包含在/中的F：D（F）是Hilbert空间X和Y之间的非线性算子.在非线性算子F和未知解x的光滑性满足一定条件的情况下，给出了该方法的收敛性和稳定性估计，证明了当正则化参数由广义偏差原理选择时，渐近正则化方法的精度是阶最优的.
We investigate the method of asymptotical regularization for solving nonlinear ill-posed problems F(x)=y, where, instead of y, noisy data ydelta epsilon Y with //y-ydelta //<or= delta are given and F:D(F) contained in/implied by X to Y is a nonlinear operator between Hilbert spaces X and Y. Assuming certain conditions concerning the nonlinear operator F and the smoothness of the unknown solution x we give convergence properties of the method and derive stability estimates, which show that the accuracy of the asymptotical regularization method is order optimal provided that the regularization parameter has been chosen by a generalized discrepancy principle.