Volume 28, Issue 6
Error Estimates for the Recursive Linearization of Inverse Medium Problems

J. Comp. Math., 28 (2010), pp. 725-744.

Published online: 2010-12

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• 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.

• Keywords

Recursive linearization, Tikhonov regularization, Inverse problems, Convergence analysis.

• AMS Subject Headings

35R30, 65N30, 78A46

• Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-28-725, author = {}, title = {Error Estimates for the Recursive Linearization of Inverse Medium Problems}, journal = {Journal of Computational Mathematics}, year = {2010}, volume = {28}, number = {6}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1003-m0004}, url = {http://global-sci.org/intro/article_detail/jcm/8547.html} }
TY - JOUR T1 - Error Estimates for the Recursive Linearization of Inverse Medium Problems 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 -

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.

Gang Bao & Faouzi Triki. (1970). Error Estimates for the Recursive Linearization of Inverse Medium Problems. Journal of Computational Mathematics. 28 (6). 725-744. doi:10.4208/jcm.1003-m0004
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