Two-Step Newton-Tikhonov Method for Hammerstein-Type Equations: Finite-Dimensional Realization

George, Santhosh and Shobha, Monnanda Erappa (2012) Two-Step Newton-Tikhonov Method for Hammerstein-Type Equations: Finite-Dimensional Realization. ISRN Applied Mathematics. pp. 1-22. ISSN 2090-5572

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Abstract

Finite-dimensional realization of a Two-Step Newton-Tikhonov method is considered for obtaining a stable approximate solution to nonlinear ill-posed Hammerstein-type 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

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