Secant-type iteration for nonlinear ill-posed equations in Banach space
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Date
2023
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Publisher
De Gruyter Open Ltd
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. © 2022 Walter de Gruyter GmbH, Berlin/Boston 2023.
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Keywords
Nonlinear equations, Parameterization, 47h06, 47j05, 47j06, 49j30, 65j20, Adaptive parameter choice strategy, Adaptive parameters, Iterative schemes, Lavrentiev regularizations, Nonlinear ill-posed problems, Parameter choice, Secant-type iterative scheme, Banach spaces
Citation
Journal of Inverse and Ill-Posed Problems, 2023, 31, 1, pp. 147-157