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Title: Weighted Regularization Methods for Ill-Posed Problems
Authors: Kanagaraj, K.
Supervisors: George, Santhosh
Keywords: Department of Mathematical and Computational Sciences;Ill-Posed Problem;Regularization parameter;Discrepancy principle;Fractional Tikhonov regularization method;Monotone Operator;Lavrentiev Regularization;Hilbert Scales;Adaptive Parameter Choice Strategy
Issue Date: 2020
Publisher: National Institute of Technology Karnataka, Surathkal
Abstract: This thesis is devoted for obtaining a stable approximate solution for ill-posed operator equation F x = y: In the second Chapter we consider a non-linear illposed equation F x = y; where F is monotone operator defined on a Hilbert space. Our analysis in Chapter 2 is in the setting of a Hilbert scale. In the rest of the thesis, we studied weighted or fractional regularization method for linear ill-posed equation. Precisely, in Chapter 3 we studied fractional Tikhonov regularization method and in Chapters 4 and 5 we studied fractional Lavrentiv regularization method for the linear ill-posed equation A x = y; where A is a positive self-adjoint operator. Numerical examples are provided to show the reliability and effectiveness of our methods.
Appears in Collections:1. Ph.D Theses

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