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

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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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Acknowledgements

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.

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Authors and Affiliations

  1. Department of Mathematical and Computational Sciences, National Institute of Technology, Mangaluru, Karnataka, 575 025, India

    K. Kanagaraj & Santhosh George

  2. Department of Mechanical and Aerospace Engineering, IIT Hyderabad, Sangareddy, Telangana, 502285, India

    G. D. Reddy

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  1. K. Kanagaraj
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Correspondence to Santhosh George.

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Kanagaraj, K., Reddy, G.D. & George, S. Discrepancy principles for fractional Tikhonov regularization method leading to optimal convergence rates. J. Appl. Math. Comput. 63, 87–105 (2020). https://doi.org/10.1007/s12190-019-01309-3

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