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An iterative method and its application to stable inversion

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Abstract

In this paper, we study convergence and data dependence of SP and normal-S iterative methods for the class of almost contraction mappings under some mild conditions. The validity of these theoretical results is confirmed with numerical examples. It has been observed that a special case of SP iterative method, namely normal-S iterative method, performs better and so the latter is implemented in the stable inversion of nonlinear discrete time dynamical systems to yield convergence results when Picard iterative method diverges. This is also illustrated with a numerical example. Our work extends and improves upon many results existing in the literature.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments to improve quality and presentation of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Adiyaman University, 02040, Adiyaman, Turkey

    Faik Gürsoy

  2. Department of Mechanical and Aeronautical Engineering, University of Pretoria, Pretoria, South Africa

    Johannes Jacobus Arnoldi Eksteen

  3. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Abdul Rahim Khan

  4. Department of Mathematical Engineering, Yildiz Technical University, 34210, Istanbul, Turkey

    Vatan Karakaya

Authors
  1. Faik Gürsoy
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  2. Johannes Jacobus Arnoldi Eksteen
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  3. Abdul Rahim Khan
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  4. Vatan Karakaya
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Correspondence to Faik Gürsoy.

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Communicated by V. Loia.

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Gürsoy, F., Eksteen, J.J.A., Khan, A.R. et al. An iterative method and its application to stable inversion. Soft Comput 23, 7393–7406 (2019). https://doi.org/10.1007/s00500-018-3384-6

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