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On the convergence of a regularizing Levenberg–Marquardt scheme for nonlinear ill-posed problems

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Abstract

In this note, we study the convergence of the Levenberg–Marquardt regularization scheme for nonlinear ill-posed problems. We consider the case that the initial error satisfies a source condition. Our main result shows that if the regularization parameter does not grow too fast (not faster than a geometric sequence), then the scheme converges with optimal convergence rates. Our analysis is based on our recent work on the convergence of the exponential Euler regularization scheme (Hochbruck et al. in Inverse Probl 25(7):075009, 2009).

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Authors and Affiliations

  1. Mathematisches Institut, Heinrich-Heine Universität Düsseldorf, 40225, Düsseldorf, Germany

    Marlis Hochbruck & Michael Hönig

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  1. Marlis Hochbruck
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  2. Michael Hönig
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Correspondence to Marlis Hochbruck.

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Hochbruck, M., Hönig, M. On the convergence of a regularizing Levenberg–Marquardt scheme for nonlinear ill-posed problems. Numer. Math. 115, 71–79 (2010). https://doi.org/10.1007/s00211-009-0268-9

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  • DOI: https://doi.org/10.1007/s00211-009-0268-9

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