Two-step newton-tikhonov method for Hammerstein-type equations : finite-dimensional realization
Joint Authors
Shobha, Monnanda Erappa
George, Santhosh
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-22, 22 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-05-08
Country of Publication
Egypt
No. of Pages
22
Main Subjects
Abstract EN
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 Fréchet derivative of F at an initial approximation x0 of the the solution x̂: 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.
American Psychological Association (APA)
George, Santhosh& Shobha, Monnanda Erappa. 2012. Two-step newton-tikhonov method for Hammerstein-type equations : finite-dimensional realization. ISRN Applied Mathematics،Vol. 2012, no. 2012, pp.1-22.
https://search.emarefa.net/detail/BIM-497735
Modern Language Association (MLA)
George, Santhosh& Shobha, Monnanda Erappa. Two-step newton-tikhonov method for Hammerstein-type equations : finite-dimensional realization. ISRN Applied Mathematics No. 2012 (2012), pp.1-22.
https://search.emarefa.net/detail/BIM-497735
American Medical Association (AMA)
George, Santhosh& Shobha, Monnanda Erappa. Two-step newton-tikhonov method for Hammerstein-type equations : finite-dimensional realization. ISRN Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-22.
https://search.emarefa.net/detail/BIM-497735
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references : p. 21-22
Record ID
BIM-497735