Simplified Generalized Gauss Newton Method for Nonlinear Ill-Posed Operator Equations in Hilbert Scales

被引：5

作者：

Mahale, Pallavi ^{[1
]}

Dadsena, Pradeep Kumar ^{[2
]}

机构：

[1] Visvesvaraya Natl Inst Technol Nagpur, Dept Math, Nagpur 440010, Maharashtra, India

[2] Govt Engn Coll Jagdalpur, Bastar 494001, Chattishgarah, India

来源：

COMPUTATIONAL METHODS IN APPLIED MATHEMATICS | 2018年 / 18卷 / 04期

关键词：

Nonlinear Ill-Posed Operator Equations; Iterative Regularization Methods; Hilbert Scale; Stopping Index; PARAMETER CHOICE STRATEGIES; TIKHONOV REGULARIZATION; DISCREPANCY PRINCIPLE; ERROR-BOUNDS;

D O I：

10.1515/cmam-2017-0045

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the simplified generalized Gauss-Newton method in a Hilbert scale setting to get an approximate solution of the ill-posed operator equation of the form F(x) = y where F : D(F) subset of X -> Y is a nonlinear operator between Hilbert spaces X and Y. Under suitable nonlinearly conditions on F, we obtain an order optimal error estimate under the Morozov type stopping rule.

引用

页码：687 / 702

页数：16

共 21 条

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[2]

BAKUSHINSKIY A. B., 1992, IMA J NUMER ANAL, V32, P1503

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