Faculty Publications

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Author: search.filters.author.Erappa, M.E.Subject: search.filters.subject.Monotone operator

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    Finite dimensional realization of a Guass-Newton method for ill-posed hammerstein type operator equations
    (2012) Erappa, M.E.; George, S.
    Finite dimensional realization of an iterative regularization method for approximately solving the non-linear ill-posed Hammerstein type operator equations KF(x) = f, is considered. The proposed method is a combination of the Tikhonov regularization and Guass-Newton method. The advantage of the proposed method is that, we use the Fr chet derivative of F only at one point in each iteration. We derive the error estimate under a general source condition and the regularization parameter is chosen according to balancing principle of Pereverzev and Schock (2005). The derived error estimate is of optimal order and the numerical example provided proves the efficiency of the proposed method. © 2012 Springer-Verlag.
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    Dynamical system method for ill-posed Hammerstein type operator equations with monotone operators
    (2012) Erappa, M.E.; George, S.
    The problem of approximately solving an ill-posed Hammerstein type operator equation KF(x) = y in a Hilbert space is considered, where K is a bounded linear operator and F is a non-linear monotone operator. The method involves the Dynamical System Method (DSM) - both continuous and iterative schemes, studied by Ramm (2005), and known as Tikhonov regularization. By choosing the regularization parameter according to an adaptive scheme considered by Pereverzev and Schock (2005) an order optimal error estimate has been obtained. © 2012 Academic Publications, Ltd.
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    Expanding the applicability of a two step Newton-type projection method for ILL-posed problems
    (Adam Mickiewicz University Press Nowowiejskiego 55 Poznan 61-734, 2014) Argyros, I.K.; Erappa, M.E.; George, S.
    There are many classes of ill-posed problems that cannot be solved with existing iterative methods, since the usual Lipschitz-type assumptions are not satisfied. In this study, we expand the applicability of a two step Newton-type projection method considered in [10], [11], using weaker assumptions. Numerical examples for the method and examples where the old assumptions are not satisfied but the new assumptions are satisfied are provided at the end of this study.