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A regularization Levenberg-Marquardt scheme, with applications to inverse groundwater filtration problems

  • The first part of this paper studies a Levenberg-Marquardt scheme for nonlinear inverse problems where the corresponding Lagrange (or regularization) parameter is chosen from an inexact Newton strategy. While the convergence analysis of standard implementations based on trust region strategies always requires the invertibility of the Fréchet derivative of the nonlinear operator at the exact solution, the new Levenberg-Marquardt scheme is suitable for ill-posed problems as long as the Taylor remainder is of second order in the interpolating metric between the range and dornain topologies. Estimates of this type are established in the second part of the paper for ill-posed parameter identification problems arising in inverse groundwater hydrology. Both, transient and steady state data are investigated. Finally, the numerical performance of the new Levenberg-Marquardt scheme is studied and compared to a usual implementation on a realistic but synthetic 2D model problem from the engineering literature.
Author:Martin Hanke
URN (permanent link):urn:nbn:de:hbz:386-kluedo-48611
Serie (Series number):Preprints (rote Reihe) des Fachbereich Mathematik (283)
Document Type:Report
Language of publication:English
Publication Date:2017/10/16
Year of Publication:1996
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2017/10/16
Number of page:18
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
Licence (German):Creative Commons 4.0 - Namensnennung, nicht kommerziell, keine Bearbeitung (CC BY-NC-ND 4.0)