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.
Funding source: National Board for Higher Mathematics
Award Identifier / Grant number: 020111/17/2020
Funding statement: The work of Santhosh George is supported by National Board of Higher Mathematics (NBHM), No. 020111/17/2020 NBHM (R.P.)/R & D II/8073.
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- Stability for the electromagnetic inverse source problem in inhomogeneous media
- Scalar and vector tomography for the weighted transport equation with application to helioseismology
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