Startseite Convergence analysis of Inexact Newton–Landweber iteration with frozen derivative in Banach spaces
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Convergence analysis of Inexact Newton–Landweber iteration with frozen derivative in Banach spaces

  • Gaurav Mittal EMAIL logo und Ankik Kumar Giri
Veröffentlicht/Copyright: 27. Juni 2023

Abstract

In this paper, we study the convergence analysis of the inexact Newton–Landweber iteration method (INLIM) with frozen derivative in Hilbert as well as Banach spaces. To study the convergence analysis, we incorporate the Hölder stability of the inverse mapping and Lipschitz continuity of the Fréchet derivative of the forward mapping. Moreover, we derive the convergence rates of INLIM in Hilbert as well as Banach spaces without using any extra smoothness condition. Finally, we compare our convergence rates results with that of several other frozen methods proposed in the literature to solve inverse problems.

MSC 2020: 65J15; 65J20; 47H17

Funding statement: The work of Ankik Kumar Giri is supported by the grant CRG/2022/005491 of SERB, India.

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Received: 2023-01-14
Revised: 2023-03-26
Accepted: 2023-05-27
Published Online: 2023-06-27
Published in Print: 2024-06-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 26.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/jiip-2023-0002/html
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