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Extended Newton-type Iteration for Nonlinear Ill-posed Equations in Banach Space

Publication Type : Journal Article

Publisher : Journal of Applied Mathematics and Computing

Authors : Dr. Sreedeep C. D., George, Santhosh; Argyros, Ioannis K.

Source : Journal of Applied Mathematics and Computing, Volume 60, Number 1, p.435–453 (2019)

Url : https://doi.org/10.1007/s12190-018-01221-2

Keywords : adaptive parameter choice strategy, Banach space, Extended Newton iterative scheme, Lavrentiev regularization, m-Accretive mappings, nonlinear ill-posed problem

Campus : Amritapuri

School : School of Arts and Sciences

Department : Mathematics

Year : 2019

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.

Cite this Research Publication : Sreedeep C. D., George, S., and Argyros, I. K., “Extended Newton-type Iteration for Nonlinear Ill-posed Equations in Banach Space”, Journal of Applied Mathematics and Computing, vol. 60, pp. 435–453, 2019.

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