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Extended Newton-type iteration for nonlinear ill-posed equations in Banach space

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Abstract

In this paper, we study nonlinear ill-posed equations involving m-accretive mappings in Banach spaces. We produce an extended Newton-type iterative scheme that converges cubically to the solution which uses assumptions only on the first Fréchet derivative of the operator. Using general Hölder type source condition we obtain an error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060–2076, 2005) for choosing the regularization parameter.

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Acknowledgements

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. Sreedeep would like to thank National Institute of Technology Karnataka, India, for the financial support.

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Authors and Affiliations

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

    C. D. Sreedeep & Santhosh George

  2. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

Authors
  1. C. D. Sreedeep
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  2. Santhosh George
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  3. Ioannis K. Argyros
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Correspondence to C. D. Sreedeep.

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Sreedeep, C.D., George, S. & Argyros, I.K. Extended Newton-type iteration for nonlinear ill-posed equations in Banach space. J. Appl. Math. Comput. 60, 435–453 (2019). https://doi.org/10.1007/s12190-018-01221-2

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  • DOI: https://doi.org/10.1007/s12190-018-01221-2

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