Logarithmic convergence rate of Levenberg–Marquardt method with application to an inverse potential problem

Christine Böckmann 1 , Athassawat Kammanee 2 , and Andreas Braunß 1
  • 1 Institute of Mathematics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany.
  • 2 Department of Mathematics, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90112, Thailand.

Abstract

We prove logarithmic convergence rate of the Levenberg–Marquardt method in a Hilbert space if a logarithmic source condition is satisfied. This method is applied to an inverse potential problem. Numerical implementations demonstrate the convergence rate.

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