IJPAM: Volume 83, No. 5 (2013)

PROJECTION METHOD FOR NEWTON-TIKHONOV
REGULARIZATION FOR NON-LINEAR ILL-POSED
HAMMERSTEIN TYPE OPERATOR EQUATIONS

Monnanda Erappa Shobha, Santhosh George
Department of Mathematical and Computational Sciences
National Institute of Technology Karnataka
575 025, INDIA

Proceedings of
NCRTMSA - 2012


Abstract. An iteratively regularized projection scheme for the ill-posed Hammerstein type operator equation KF(x)=f has been considered. Here F:D(F)⊆ X→ X is a non-linear operator, K:X→ Y is a bounded linear operator, X and Y are Hilbert spaces. The method is a combination of discretized Tikhonov regularization and modified Newton's method. It is assumed that the Frechet derivative of F at x0 is invertible i.e., the ill-posedness of the operator KF is due to the ill-posedness of the linear operator K. Here x0 is an initial approximation to the solution x of KF(x)=f. Adaptive choice of the parameter suggested by Perverzev and Schock(2005) is employed in selecting the regularization parameter α. A numerical example is given to test the reliability of the method.

Received: January 10, 2013

AMS Subject Classification: 47J06, 47A52, 65N20, 65J20

Key Words and Phrases: discretized Newton Tikhonov method, ill-posed Hammerstein operator, balancing principle, regularization

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DOI: 10.12732/ijpam.v83i5.6 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 83
Issue: 5