Derivative Free Iterative Scheme for Monotone Nonlinear Ill-posed Hammerstein-Type Equations

An iterative scheme which is free of derivative is employed to approximately solve nonlinear ill-posed Hammerstein type operator equations TG (x) = y, where G is a nonlinear monotone operator and T is a bounded linear operator defined on Hilbert spaces X, Y, Z. The convergence analysis adapted in th...

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Bibliographic Details
Published in:IAENG international journal of applied mathematics 2021-03, Vol.51 (1), p.1-5
Main Authors: Erappa, Shobha M, George, Santhosh
Format: Article
Language:English
Subjects:
Hilbert space
Ill posed problems
Iterative methods
Linear operators
Lipschitz condition
Regularization
Online Access:Get full text
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Summary:An iterative scheme which is free of derivative is employed to approximately solve nonlinear ill-posed Hammerstein type operator equations TG (x) = y, where G is a nonlinear monotone operator and T is a bounded linear operator defined on Hilbert spaces X, Y, Z. The convergence analysis adapted in the paper includes weaker Lipschitz condition and adaptive choice of Perverzev and Schock(2005) is employed to choose the regularization parameter a. Furthermore, order optimal error bounds are obtained and the method is validated by a numerical example.
ISSN:1992-9978
1992-9986