Please use this identifier to cite or link to this item: https://idr.l3.nitk.ac.in/jspui/handle/123456789/14125
Title: Steepest Descent Type Methods for Nonlinear Ill-Posed Operator Equations
Authors: M, Sabari
Supervisors: George, Santhosh
Keywords: Department of Mathematical and Computational Sciences;Ill-posed nonlinear equations;Steepest descent method;Minimal error method;Regularization method;Tikhonov regularization;Discrepancy principle;Balancing principle
Issue Date: 2018
Publisher: National Institute of Technology Karnataka, Surathkal
Abstract: In this thesis, we consider steepest descent method and minimal error method for approximating a solution of the nonlinear ill-posed operator equation F(x) = y, where F : D(F) ⊆ X → Y is nonlinear Fr´echet differentiable operator between the Hilbert spaces X and Y. In practical application, we have only noisy data yδ with ∥y − yδ∥ ≤ δ. To our knowledge, convergence rate result for the steepest descent method and minimal error method with noisy data are not known. We provide error estimate for these methods with noisy data. We modified these methods with less computational cost. Error estimate for steepest descent method and minimal error method is not known under H¨older-type source condition. We provide an error estimate for these methods under H¨older-type source condition and also with noisy data. We also studied the regularized version of steepest descent method and regularization parameter in this regularized version is selected through the adaptive scheme of Pereverzev and Schock (2005).
URI: http://idr.nitk.ac.in/jspui/handle/123456789/14125
Appears in Collections:1. Ph.D Theses

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