We use a combination of modified Newton method and Tikhonov regularization to obtain a stable approximate solution for nonlinear ill-posed Hammerstein-type operator equations KF(x) = y. It is assumed that the available data is with , K: Z → Y is a bounded linear operator and F: X → Z is a nonlinear operator where X,Y,Z are Hilbert spaces. Two cases of F are considered: where exists (F’(x₀) is the Fréchet derivative of F at an initial guess x₀) and where F is a monotone operator. The parameter choice using an a priori and an adaptive choice under a general source condition are of optimal order. The computational results provided confirm the reliability and effectiveness of our method.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am41-1-9,
author = {Monnanda Erappa Shobha and Ioannis K. Argyros and Santhosh George},
title = {Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations},
journal = {Applicationes Mathematicae},
volume = {41},
year = {2014},
pages = {107-129},
zbl = {1307.47072},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-1-9}
}
Monnanda Erappa Shobha; Ioannis K. Argyros; Santhosh George. Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations. Applicationes Mathematicae, Tome 41 (2014) pp. 107-129. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am41-1-9/