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Numerical Algorithms

, Volume 68, Issue 2, pp 289–304 | Cite as

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

  • Vorkady S. Shubha
  • Santhosh George
  • P. Jidesh
Original Paper

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.

Keywords

Iterative method Quadratic convegence Derivative free method Nonlinear ill-posed equations Lavrentiev regularization Adaptive method 

Mathematics Subject Classifications (2010)

41H25 65F22 65J15 65J22 47A52 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Vorkady S. Shubha
    • 1
  • Santhosh George
    • 1
  • P. Jidesh
    • 1
  1. 1.Department of Mathematical and Computational SciencesNational Institute of Technology KarnatakaMangaloreIndia

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