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