Improved local convergence analysis of the Landweber iteration in Banach spaces

The convergence analysis of the Landweber iteration for solving inverse problems in Banach spaces via Hölder stability estimates is well studied by de Hoop et al. (Inverse Probl 28(4):045001, 2012) in the presence of unperturbed data. For real life problems, it is important to study the convergence...

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Bibliographic Details
Published inArchiv der Mathematik Vol. 120; no. 2; pp. 195 - 202
Main Authors Mittal, Gaurav, Giri, Ankik Kumar
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.02.2023
Springer Nature B.V
Subjects
Banach spaces
Convergence
Estimates
Inverse problem theory
Mathematics
Mathematics and Statistics
Smoothness
Stability
Inverse problems
65J20
Regularization
47H17
65J15
Ill-posed operator equations
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Summary:The convergence analysis of the Landweber iteration for solving inverse problems in Banach spaces via Hölder stability estimates is well studied by de Hoop et al. (Inverse Probl 28(4):045001, 2012) in the presence of unperturbed data. For real life problems, it is important to study the convergence analysis in the presence of perturbed data. In this paper, we show that the convergence analysis of the Landweber iteration can also be studied by utilizing the Hölder stability estimates in the presence of perturbed data. Furthermore, as a by-product, we formulate the convergence rates of the Landweber iteration without utilizing any additional smoothness condition. This shows the advantage of Hölder stability estimates over a tangential cone condition in the theory of inverse problems.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-022-01807-0