Jump to ContentJump to Main Navigation

Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

6 Issues per year


Increased IMPACT FACTOR 2013: 0.593
Rank 143 out of 299 in category Mathematics in the 2013 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR): 0.466
Source Normalized Impact per Paper (SNIP): 1.251

Mathematical Citation Quotient 2013: 0.51

VolumeIssuePage

Issues

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: 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

Comments (0)

Please log in or register to comment.
Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.