TY - JOUR
T1 - Error Estimates for the Recursive Linearization of Inverse Medium Problems
AU - Gang Bao & Faouzi Triki
JO - Journal of Computational Mathematics
VL - 6
SP - 725
EP - 744
PY - 2010
DA - 2010/12
SN - 28
DO - http://doi.org/10.4208/jcm.1003-m0004
UR - https://global-sci.org/intro/article_detail/jcm/8547.html
KW - Recursive linearization, Tikhonov regularization, Inverse problems, Convergence analysis.
AB - <p style="text-align: justify;">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 Problems 13(1997), pp.253-282] is established for solving the acoustic inverse scattering problem.</p>