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Third-order derivative-free methods in Banach spaces for nonlinear ill-posed equations

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Abstract

We develop three third order derivative-free iterative methods to solve the nonlinear ill-posed oprerator equation \(F(x)=f\) approximately. The methods involve two steps and are free of derivatives. Convergence analysis shows that these methods converge cubically. The adaptive scheme introduced in Pereverzyev and Schock (SIAM J Numer Anal 43(5):2060–2076, 2005) has been employed to choose regularization parameter. These methods are applied to the inverse gravimetry problem to validate our developed results.

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Acknowledgements

Ms Shubha VS would like to thank NBHM, Government of India, for providing fellowship under the Post-Doctral fellowship scheme, to carry out the research activities in the department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Surathkal, India. The work of Santhosh George and Jidesh P is supported by the Science and Engineering Research Board Government of India under the Grant No: EMR2017001597.

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

    Vorkady S. Shubha, Santhosh George & P. Jidesh

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  1. Vorkady S. Shubha
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  2. Santhosh George
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  3. P. Jidesh
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Correspondence to Vorkady S. Shubha.

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Shubha, V.S., George, S. & Jidesh, P. Third-order derivative-free methods in Banach spaces for nonlinear ill-posed equations. J. Appl. Math. Comput. 61, 137–153 (2019). https://doi.org/10.1007/s12190-019-01246-1

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