Lechleiter, Armin The factorization method is independent of transmission eigenvalues. (English) Zbl 1184.78020 Inverse Probl. Imaging 3, No. 1, 123-138 (2009). Summary: As a rule of thumb, sampling methods for inverse scattering problems suffer from interior eigenvalues of the obstacle. Indeed, throughout the history of such algorithms one meets the phenomenon that if the wave number meets some resonance frequency of the scatterer, then those methods can only be shown to work under suitable modifications. Such modifications often require a-priori knowledge, corrupting thereby the main advantage of sampling methods. It was common belief that transmission eigenvalues play a role corresponding to Dirichlet or Neumann eigenvalues in this respect. We show that this is not the case for the Factorization method: when applied to inverse medium scattering problems this method is stable at transmission eigenvalues. Cited in 16 Documents MSC: 78A46 Inverse problems (including inverse scattering) in optics and electromagnetic theory 74J25 Inverse problems for waves in solid mechanics 76Q05 Hydro- and aero-acoustics 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 78M25 Numerical methods in optics (MSC2010) Keywords:factorization method; transmission eigenvalues; inverse medium scattering; acoustics; electromagnetics; range identity PDFBibTeX XMLCite \textit{A. Lechleiter}, Inverse Probl. Imaging 3, No. 1, 123--138 (2009; Zbl 1184.78020) Full Text: DOI