Newton type iteration for Tikhonov regularization of non-linear ill-posed Hammerstein type equations

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dc.contributor.authorGeorge, S.
dc.contributor.authorErappa, M.E.
dc.date.accessioned2026-02-05T09:34:17Z
dc.date.issued2014
dc.description.abstractAn iterative method is investigated for a nonlinear ill-posed Hammerstein type operator equation KF(x)=f. We use a center-type Lipschitz condition in our convergence analysis instead of the usual Lipschitz condition. The adaptive method of Pereverzev and Schock (SIAM J. Numer. Anal. 43(5):2060-2076, 2005) is used for choosing the regularization parameter. The optimality of this method is proved under a general source condition involving the Fréchet derivative of F at some initial guess x <inf>0</inf>. A numerical example of nonlinear integral equation shows the efficiency of this procedure. © 2013 Korean Society for Computational and Applied Mathematics.
dc.identifier.citationJournal of Applied Mathematics and Computing, 2014, 44, 46054, pp. 69-82
dc.identifier.issn15985865
dc.identifier.urihttps://doi.org/10.1007/s12190-013-0681-1
dc.identifier.urihttps://idr.nitk.ac.in/handle/123456789/26532
dc.subjectAdaptive choice
dc.subjectGauss-Newton methods
dc.subjectHammerstein
dc.subjectIterative regularization
dc.subjectNonlinear ill-posed problems
dc.subjectTikhonov regularization
dc.subjectMathematical operators
dc.subjectNewton-Raphson method
dc.subjectProblem solving
dc.titleNewton type iteration for Tikhonov regularization of non-linear ill-posed Hammerstein type equations

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