Numerical Algorithms

, Volume 68, Issue 2, pp 289–304

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

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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