Numerische Mathematik

, Volume 115, Issue 1, pp 71–79 | Cite as

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

Article

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).

Mathematics Subject Classification (2000)

65J15 65J20 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Mathematisches InstitutHeinrich-Heine Universität DüsseldorfDüsseldorfGermany

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