A posteriori stopping rule for regularized fixed point iterations

被引：8

作者：

Bakushinsky, A

Smirnova, A ^{[1
]}

机构：

[1] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

[2] RAS, Inst Syst Anal, Moscow 117312, Russia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2006年 / 64卷 / 06期

基金：

美国国家科学基金会;

关键词：

discrepancy principle; ill-posed problem; regularization;

D O I：

10.1016/j.na.2005.06.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Iteratively regularized fixed-point iteration scheme x(n+1) = x(n) - alpha(n) {F(x(n)) - f(delta) + epsilon(n) (x(n) - x(0))} combined with the generalized discrepancy principle parallel to F(x(N)) - f(delta)parallel to(2) <= tau(delta) < parallel to F(x(n)) - f(delta)parallel to(2), 0 <= n < N, tau > 1, for solving nonlinear operator equation F(x) = f in a Hilbert space is studied in the paper. It is shown that if F is monotone and Lipschitz-continuous the sequence {N(delta)} is admissible, i.e. (delta -> 0)lim parallel to x(N(delta)) - x*parallel to = 0, where x* is a solution to F(x) = f. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：1255 / 1261

页数：7

共 8 条

[1] On application of generalized discrepancy principle to iterative methods for nonlinear ill-posed problems [J].