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Expanding the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems

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Abstract

We expand the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of the nonlinear ill-posed problem presented in Jin and Hou (Numer Math 83:139–159, 1999) by weakening the conditions needed in Jin and Hou [13]. Using a center-type Lipschitz condition instead of a Lipschitz-type condition used in Jin and Hou [13], Scherzer et al. (SIAM J Numer Anal 30:1796–1838, 1993), we obtain a tighter convergence analysis. Numerical examples are presented to show that our results apply but earlier ones do not apply to solve equations.

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Acknowledgements

The research work was supported by the National Natural Science Foundation of China (11771067) and the Applied Basic Project of Sichuan Province (2019YJ0204).

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Authors and Affiliations

  1. Department of Mathematicsal Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Yeol Je Cho & Yi-bin Xiao

  3. Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea

    Yeol Je Cho

  4. Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangalore, 757 025, India

    Santhosh George

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  1. Ioannis K. Argyros
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  2. Yeol Je Cho
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  3. Santhosh George
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  4. Yi-bin Xiao
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Correspondence to Yeol Je Cho.

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Argyros, I.K., Cho, Y.J., George, S. et al. Expanding the applicability of an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems. RACSAM 113, 2813–2826 (2019). https://doi.org/10.1007/s13398-019-00657-w

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  • DOI: https://doi.org/10.1007/s13398-019-00657-w

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