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Secant-type iteration for nonlinear ill-posed equations in Banach space

Publication Type : Journal Article

Source : Journal of Inverse and Ill-posed Problems

Url : https://www.degruyter.com/document/doi/10.1515/jiip-2021-0019/html

Campus : Amritapuri

School : School of Physical Sciences

Department : Mathematics

Year : 2023

Abstract : In this paper, we study secant-type iteration for nonlinear ill-posed equations involving 𝑚-accretive mappings in Banach spaces. We prove that the proposed iterative scheme has a convergence order at least 2.20557 using assumptions only on the first Fréchet derivative of the operator. Further, using a general Hölder-type source condition, we obtain an optimal error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter.

Cite this Research Publication : George, Santhosh, Sreedeep, C. D. and Argyros, Ioannis K.. "Secant-type iteration for nonlinear ill-posed equations in Banach space" Journal of Inverse and Ill-posed Problems, vol. 31, no. 1, 2023, pp. 147-157

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