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Publication Date:
August 2011
ISSN:
1569-3945
DOI:
10.1515/jiip.2011.034

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Journal of Inverse and III-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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

1 / 2 / 1

1Institute of Mathematics, University of Potsdam, Am Neuen Palais 10, 14469 Potsdam, Germany.

2Department of Mathematics, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90112, Thailand.

Citation Information: Journal of Inverse and Ill-posed Problems. Volume 19, Issue 3, Pages 345–367, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: 10.1515/jiip.2011.034, August 2011

Publication History:
Received:
2010-03-06
Published Online:
2011-08-05

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

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