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

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.