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A derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations

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Abstract

In this work, we develop a derivative free iterative method for the implementation of Lavrentiev regularization for approximately solving the nonlinear ill-posed operator equation F(x) = y. Convergence analysis shows that the method converges quadratically. Apart from being totally free of derivatives, the method, under a general source condition provide an optimal order error estimate. We use the adaptive method introduced in Pereverzyev and Schock (SIAM J. Numer. Anal. 43, 2060–2076, 2005) for choosing the regularization parameter. In the concluding section the method is applied to numerical solution of the inverse gravimetry problem.

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Authors and Affiliations

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

    Vorkady S. Shubha, Santhosh George & P. Jidesh

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

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Shubha, V.S., George, S. & Jidesh, P. A derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations. Numer Algor 68, 289–304 (2015). https://doi.org/10.1007/s11075-014-9844-x

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  • DOI: https://doi.org/10.1007/s11075-014-9844-x

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