Year: 2010
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 6 : pp. 725–744
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1003-m0004
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 6 : pp. 725–744
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Recursive linearization Tikhonov regularization Inverse problems Convergence analysis.