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Error Estimates for the Recursive Linearization of Inverse Medium Problems

Error Estimates for the Recursive Linearization of Inverse Medium Problems
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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.

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