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

Christine Böckmann; Athassawat Kammanee; Andreas Braunß

doi:10.1515/jiip.2011.034

Published by De Gruyter August 5, 2011

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

Christine Böckmann , Athassawat Kammanee and Andreas Braunß

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https://doi.org/10.1515/jiip.2011.034

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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.

Keywords.: Levenberg–Marquardt method; inverse potential problems; logarithmic convergence rate; discrepancy principle; logarithmic source condition

Received: 2010-03-06

Published Online: 2011-08-05

Published in Print: 2011-August

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

Abstract

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