Derivative Free Iterative Scheme for Monotone Nonlinear Ill-posed Hammerstein-Type Equations
No Thumbnail Available
Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
International Association of Engineers
Abstract
An iterative scheme which is free of derivative is employed to approximately solve nonlinear ill-posed Hammer-stein type operator equations )TG(x) = Y, where G is a non-linear monotone operator and ) 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 U. Furthermore, order optimal error bounds are obtained and the method is validated by a numerical example. © 2021, IAENG International Journal of Applied Mathematics. All Rights Reserved.
Description
Keywords
Convergence of numerical methods, Error analysis, Iterative methods, Mathematical operators, Bounded linear operators, Convergence analysis, Iterative schemes, Lipschitz conditions, Monotone operators, Operator equation, Optimal error bound, Regularization parameters, Nonlinear equations
Citation
IAENG International Journal of Applied Mathematics, 2021, 51, 1, pp. -