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# Computational Methods in Applied Mathematics

Editor-in-Chief: Carstensen, Carsten

Managing Editor: Matus, Piotr

4 Issues per year

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Volume 18, Issue 4

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

Pallavi Mahale
• Corresponding author
• Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur, Nagpur, Maharashtra 440010, India
• Email
• Other articles by this author:
Published Online: 2017-10-27 | DOI: https://doi.org/10.1515/cmam-2017-0045

## Abstract

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 $F\left(x\right)=y$ where $F:D\left(F\right)\subseteq X\to Y$ 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.

MSC 2010: 47A52; 65F22; 65J15; 65J22; 65M30

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Revised: 2017-09-08

Accepted: 2017-09-27

Published Online: 2017-10-27

Published in Print: 2018-10-01

Citation Information: Computational Methods in Applied Mathematics, Volume 18, Issue 4, Pages 687–702, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840,

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