Vol. 10, No. 3, 2015

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The reciprocity likelihood maximization: a variational approach of the reciprocity gap method

Stéphane Andrieux

Vol. 10 (2015), No. 3, 219–237
DOI: 10.2140/jomms.2015.10.219

We introduce a new concept allowing the recasting of the reciprocity gap method into a variational method. The reciprocity likelihood functional maximization gives rise to nested approximation properties when performed on minimization spaces with increasing dimensions and leads to direct identification methods grounded on the reciprocity property. Application to the identification of point sources is given for illustration of the solution procedure of identification, and an analysis of the effect of noisy data shows that the proposed methods exhibit very good robustness.

inverse problems, reciprocity gap, sources identification
Received: 12 February 2014
Revised: 6 November 2014
Accepted: 25 December 2014
Published: 26 August 2015
Stéphane Andrieux
Laboratoire de Mécanique des Structures Industrielles Durables
1 Avenue du Général de Gaulle
92141 Clamart