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

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dc.contributor.authorShubha, V.S.
dc.contributor.authorGeorge, S.
dc.contributor.authorPadikkal, P.
dc.date.accessioned2026-02-05T09:33:52Z
dc.date.issued2015
dc.description.abstractIn 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. © 2014, Springer Science+Business Media New York.
dc.identifier.citationNumerical Algorithms, 2015, 68, 2, pp. 289-304
dc.identifier.issn10171398
dc.identifier.urihttps://doi.org/10.1007/s11075-014-9844-x
dc.identifier.urihttps://idr.nitk.ac.in/handle/123456789/26343
dc.publisherKluwer Academic Publishers
dc.subjectAdaptive method
dc.subjectDerivative free method
dc.subjectIterative method
dc.subjectLavrentiev regularization
dc.subjectNonlinear ill-posed equations
dc.subjectQuadratic convegence
dc.titleA derivative free iterative method for the implementation of Lavrentiev regularization method for ill-posed equations

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