Journal
JOURNAL OF COMPUTATIONAL MATHEMATICS
Volume 28, Issue 6, Pages 725-744Publisher
VSP BV
DOI: 10.4208/jcm.1003-m0004
Keywords
Recursive linearization; Tikhonov regularization; Inverse problems; Convergence analysis
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Funding
- NSF [DMS-0604790, DMS-0908325 CCF-0830161, EAR-0724527]
- ONR [N000140210365]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [0968360] Funding Source: National Science Foundation
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [0830161] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [908325] Funding Source: National Science Foundation
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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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