Fixed-point iterations in determining a Tikhonov regularization parameter in Kirsch's factorization method

DOI10.1016/j.amc.2010.05.036zbMath1197.78036OpenAlexW2097869231MaRDI QIDQ988634

Koung Hee Leem, George Pelekanos, Fermin S. Viloche Bazán

Publication date: 18 August 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.05.036

zbMATH Keywords

Tikhonov regularizationinverse scattering problemsL-curve criterionKirch's factorization method

Mathematics Subject Classification ID

Ill-posedness and regularization problems in numerical linear algebra (65F22) Inverse problems (including inverse scattering) in optics and electromagnetic theory (78A46)

Related Items (5)

A maximum product criterion as a Tikhonov parameter choice rule for Kirsch's factorization method ⋮ On a generalization of Regińska's parameter choice rule and its numerical realization in large-scale multi-parameter Tikhonov regularization ⋮ Using the linear sampling method and an improved maximum product criterion for the solution of the electromagnetic inverse medium problem ⋮ Sampling method based projection approach for the reconstruction of 3D acoustically penetrable scatterers ⋮ Simple and efficient determination of the Tikhonov regularization parameter chosen by the generalized discrepancy principle for discrete ill-posed problems

Cites Work

• Limitations of the \(L\)-curve method in ill-posed problems
• Shape reconstruction of a 2D-elastic penetrable object via the L-curve method
• Fixed-point iterations in determining the Tikhonov regularization parameter
• An improved fixed-point algorithm for determining a Tikhonov regularization parameter
• Characterization of the shape of a scattering obstacle using the spectral data of the far field operator
• A simple method using Morozov's discrepancy principle for solving inverse scattering problems
• Why linear sampling works
• A simple method for solving inverse scattering problems in the resonance region
• A Regularization Parameter in Discrete Ill-Posed Problems
• Inverse acoustic and electromagnetic scattering theory

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