Error Estimates for Recursive Linearization of Inverse Medium Problems

Gang Bao (1) , Faouzi Triki (2)

1 Department of Mathematics
2 EDP - Equations aux Dérivées Partielles

This paper is devoted to the mathematical analysis of a general recursive linearization algorithm for solving inverse medium problems with multi-frequency measurements. Under some reasonable assumptions, it is shown that the algorithm is convergent with error estimates. The work is motivated by our effort to analyze recent significant numerical results for solving inverse medium problems. Based on the uncertainty principle, the recursive linearization allows the nonlinear inverse problems to be reduced to a set of linear problems and be solved recursively in a proper order according to the measurements. As an application, the convergence of the recursive linearization algorithm [Chen, Inverse Problems13(1997), pp.253-282] is established for solving the acoustic inverse scattering problem.

Mots clés: Recursive linearization; Tikhonov regularization; Inverse problems; Convergence analysis

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Gang Bao, Faouzi Triki. Error Estimates for Recursive Linearization of Inverse Medium Problems. Journal of Computational Mathematics -International Edition-, 2010, 28 (6), pp.725-744. ⟨10.4208/jcm.1003-m0004⟩. ⟨hal-00748025⟩