Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations

Monnanda Erappa Shobha, Ioannis K. Argyros, and Santhosh George. "Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations." Applicationes Mathematicae 41.1 (2014): 107-129. <http://eudml.org/doc/286650>.

@article{MonnandaErappaShobha2014,
abstract = {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 $y^\{δ\}$ with $||y - y^\{δ\}|| ≤ δ$, 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 $F^\{\prime \}(x₀)^\{-1\}$ 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.},
author = {Monnanda Erappa Shobha, Ioannis K. Argyros, Santhosh George},
journal = {Applicationes Mathematicae},
keywords = {Newton-type iterative method; nonlinear ill-posed problems; Hammerstein operators; adaptive choice; Tikhonov regularization},
language = {eng},
number = {1},
pages = {107-129},
title = {Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations},
url = {http://eudml.org/doc/286650},
volume = {41},
year = {2014},
}

TY - JOUR
AU - Monnanda Erappa Shobha
AU - Ioannis K. Argyros
AU - Santhosh George
TI - Newton-type iterative methods for nonlinear ill-posed Hammerstein-type equations
JO - Applicationes Mathematicae
PY - 2014
VL - 41
IS - 1
SP - 107
EP - 129
AB - 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 $y^{δ}$ with $||y - y^{δ}|| ≤ δ$, 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 $F^{\prime }(x₀)^{-1}$ 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.
LA - eng
KW - Newton-type iterative method; nonlinear ill-posed problems; Hammerstein operators; adaptive choice; Tikhonov regularization
UR - http://eudml.org/doc/286650
ER -