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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


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1569-3945
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On convergence of regularized modified Newton's method for nonlinear ill-posed problems

Santhosh George1

1Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, Mangalore 575025, India. E-mail:

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 18, Issue 2, Pages 133–146, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2010.004, May 2010

Publication History

Received:
2009-12-07
Published Online:
2010-05-31

Abstract

In this paper we consider regularized modified Newton's method for approximately solving the nonlinear ill-posed problem F(x) = y, where the right hand side is replaced by noisy data yδY with ‖yyδ‖ ≤ δ and F : D(F) ⊂ XY is a nonlinear operator between Hilbert spaces X and Y. Under the assumption that Fréchet derivative F′ of F is Lipschitz continuous, a choice of the regularization parameter and a stopping rule based on a majorizing sequence are presented. We prove that under a general source condition on , the error between the regularized approximation and the solution of optimal order.

Keywords.: Tihkonov regularization; regularized Newton's method; balancing principle

Citing Articles

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[1]
Monnanda Erappa Shobha and Santhosh George
Journal of Mathematics, 2014, Volume 2014, Page 1
[2]
Ioannis K. Argyros, Santhosh George, and P. Jidesh
International Journal of Mathematics and Mathematical Sciences, 2014, Volume 2014, Page 1
[3]
V. V. Vasin
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 284, Number S1, Page 145
[4]
Santhosh George and Monnanda Erappa Shobha
Journal of Applied Mathematics and Computing, 2014, Volume 44, Number 1-2, Page 69
[5]
Santhosh George
Journal of Mathematics, 2013, Volume 2013, Page 1
[6]
Igor Kruglov, Olga Mishulina, and Murat Bakirov
Neurocomputing, 2012, Volume 96, Page 74

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