Extended Newton-type iteration for nonlinear ill-posed equations in Banach space
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Date
2019
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Publisher
Springer Verlag service@springer.de
Abstract
In this paper, we study nonlinear ill-posed equations involving m-accretive mappings in Banach spaces. We produce an extended Newton-type iterative scheme that converges cubically to the solution which uses assumptions only on the first Fréchet derivative of the operator. Using general Hölder type source condition we obtain an error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060–2076, 2005) for choosing the regularization parameter. © 2018, Korean Society for Computational and Applied Mathematics.
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Keywords
Banach spaces, Mapping, Parameterization, Adaptive parameters, Iterative schemes, Lavrentiev regularizations, M-accretive mappings, Nonlinear ill-posed problems, Nonlinear equations
Citation
Journal of Applied Mathematics and Computing, 2019, 60, 46054, pp. 435-453