Table of Contents
ISRN Applied Mathematics
Volume 2012, Article ID 728627, 14 pages
http://dx.doi.org/10.5402/2012/728627
Research Article

Two-Step Modified Newton Method for Nonlinear Lavrentiev Regularization

Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal 575025, India

Received 15 December 2011; Accepted 1 February 2012

Academic Editor: K. Djidjeli

Copyright Β© 2012 Santhosh George and Suresan Pareth. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A two step modified Newton method is considered for obtaining an approximate solution for the nonlinear ill-posed equation 𝐹(π‘₯)=𝑓 when the available data are 𝑓𝛿 with β€–π‘“βˆ’π‘“π›Ώβ€–β‰€π›Ώ and the operator 𝐹 is monotone. The derived error estimate under a general source condition on π‘₯0βˆ’Μ‚π‘₯ is of optimal order; here π‘₯0 is the initial guess and Μ‚π‘₯ is the actual solution. The regularization parameter is chosen according to the adaptive method considered by Perverzev and Schock (2005). The computational results provided endorse the reliability and effectiveness of our method.