Discrepancy principles for fractional Tikhonov regularization method leading to optimal convergence rates

Kanagaraj, K and Reddy, G D and George, Santhosh (2020) Discrepancy principles for fractional Tikhonov regularization method leading to optimal convergence rates. Journal of Applied Mathematics and Computing, 63 (1-2). ISSN 1598-5865

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Abstract

Fractional Tikhonov regularization (FTR) method was studied in the last few years for approximately solving ill-posed problems. In this study we consider the Schock-type discrepancy principle for choosing the regularization parameter in FTR and obtained the order optimal convergence rate. Numerical examples are provided in this study.

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IITH Creators:

IITH Creators	ORCiD

Item Type:

Article

Additional Information:

We would like to express our gratitude for the reviewers for their constructive criticism. The work of Santhosh George is supported by the Core Research Grant by SERB, Department of Science and Technology, Govt. of India, EMR/2017/001594. Kanagaraj would like to thank National Institute of Technology Karnataka, India, for the financial support. The work of G. D. Reddy (Post-doctoral fellow in IIT Hyderabad) is supported by the National Board of Higher Mathematics (NBHM), Mumbai, India, Grant No: 2/40(56)/2015/R&D-II/12987. The support of the NBHM is gratefully acknowledged.

Uncontrolled Keywords:

Convergence rate; Discrepancy principle; Fractional Tikhonov regularization method; Ill-posed equations; Regularization parameter

Subjects:

Physics > Mechanical and aerospace
Mathematics

Divisions:

Department of Mechanical & Aerospace Engineering

Depositing User:

Team Library

Date Deposited:

26 Dec 2019 04:05

Last Modified:

31 Oct 2022 06:47