George, Santhosh and Shobha, Monnanda Erappa (2012) TwoStep NewtonTikhonov Method for HammersteinType Equations: FiniteDimensional Realization. ISRN Applied Mathematics. pp. 122. ISSN 20905572

PDF
ISRN.pdf  Published Version Download (1MB)  Preview 
Abstract
Finitedimensional realization of a TwoStep NewtonTikhonov method is considered for obtaining a stable approximate solution to nonlinear illposed Hammersteintype operator equations KF�x� � f. Here F : D�F� ⊆ X → X is nonlinear monotone operator, K : X → Y is a bounded linear operator, X is a real Hilbert space, and Y is a Hilbert space. The error analysis for this method is done under two general source conditions, the first one involves the operator K and the second one involves the Fr´echet derivative of F at an initial approximation x0 of the the solution �x: balancing principle of Pereverzev and Schock �2005� is employed in choosing the regularization parameter and order optimal error bounds are established. Numerical illustration is given to confirm the reliability of our approach
Item Type:  Article 

Subjects:  Engineering > MIT Manipal > Mathematics 
Depositing User:  MIT Library 
Date Deposited:  26 Aug 2013 10:49 
Last Modified:  26 Aug 2013 10:49 
URI:  http://eprints.manipal.edu/id/eprint/136923 
Actions (login required)
View Item 