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The parameter choice rules for weighted Tikhonov regularization scheme

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Abstract

The well-known approach to solve the ill-posed problem is Tikhonov regularization scheme. But, the approximate solution of Tikhonov scheme may not contain all the details of the exact solution. To circumference this problem, weighted Tikhonov regularization has been introduced. In this article, we propose two a posteriori parameter choice rules to choose the regularization parameter for weighted Tikhonov regularization and establish the optimal rate of convergence \(O(\delta ^\frac{\alpha +1}{\alpha +2})\) for the scheme based on these proposed rules. The numerical results are documented to demonstrate the significance of the theoretical results.

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Acknowledgements

This manuscript is prepared by the author during NBHM post doctoral program in IIT-Hyderabad (Grant No: 2/40(56)/2015/R & D-II/12183) and the grant was supported by National board of Higher Mathematics, Mumbai, India. The support of the NBHM is gratefully acknowledged.

I thank my post doctoral advisor Dr. C. P. Vyasarayani for his valuable suggestions on this work.

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Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy, Telangana, 502285, India

    G. D. Reddy

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  1. G. D. Reddy
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Correspondence to G. D. Reddy.

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Communicated by Cristina Turner.

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Reddy, G.D. The parameter choice rules for weighted Tikhonov regularization scheme. Comp. Appl. Math. 37, 2039–2052 (2018). https://doi.org/10.1007/s40314-017-0433-1

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  • DOI: https://doi.org/10.1007/s40314-017-0433-1

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