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Iteratively regularized Landweber iteration method: Convergence analysis via Hölder stability

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  • Mittal, Gaurav
  • Giri, Ankik Kumar

Abstract

In this paper, the local convergence of Iteratively regularized Landweber iteration method is investigated for solving non-linear inverse problems in Banach spaces. Our analysis mainly relies on the assumption that the inverse mapping satisfies the Hölder stability estimate locally. We consider both noisy as well as non-noisy data in our analysis. Under the a-priori choice of stopping index for noisy data, we show that the iterates remain in a certain ball around exact solution and obtain the convergence rates. The convergence of the Iteratively regularized Landweber iterates to the exact solution is shown under certain assumptions in the case of non-noisy data and as a by-product, under different conditions, two different convergence rates are obtained.

Suggested Citation

  • Mittal, Gaurav & Giri, Ankik Kumar, 2021. "Iteratively regularized Landweber iteration method: Convergence analysis via Hölder stability," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    • Handle: RePEc:eee:apmaco:v:392:y:2021:i:c:s0096300320306974
    DOI: 10.1016/j.amc.2020.125744
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    References listed on IDEAS

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    1. Y. I. Alber & A. G. Kartsatos & E. Litsyn, 1996. "Iterative solution of unstable variational inequalities on approximately given sets," Abstract and Applied Analysis, Hindawi, vol. 1, pages 1-20, January.
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    Cited by:

    1. Mittal, Gaurav, 2024. "Nonstationary iterated frozen Tikhonov regularization with uniformly convex penalty terms for solving inverse problems," Applied Mathematics and Computation, Elsevier, vol. 468(C).
    2. Gaurav Mittal & Ankik Kumar Giri, 2022. "Novel Multi-level Projected Iteration to Solve Inverse Problems with Nearly Optimal Accuracy," Journal of Optimization Theory and Applications, Springer, vol. 194(2), pages 643-680, August.

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