Beilina, Larisa; Klibanov, Michael V. A new approximate mathematical model for global convergence for a coefficient inverse problem with backscattering data. (English) Zbl 1279.35094 J. Inverse Ill-Posed Probl. 20, No. 4, 513-565 (2012). Summary: An approximately globally convergent numerical method for a 3d coefficient inverse problem for a hyperbolic equation with backscattering data is presented. A new approximate mathematical model is presented as well. An approximation is used only on the first iteration and amounts to the truncation of a certain asymptotic series. A significantly new element of the convergence analysis is that the so-called “tail functions” are estimated. Numerical results in 2d and 3d cases are discussed, including the one for a quite heterogeneous medium. Cited in 17 Documents MSC: 35R25 Ill-posed problems for PDEs 35R30 Inverse problems for PDEs Keywords:coefficient inverse problems; approximate global convergence; new approximate mathematical model; convergence analysis; numerical studies PDFBibTeX XMLCite \textit{L. Beilina} and \textit{M. V. Klibanov}, J. Inverse Ill-Posed Probl. 20, No. 4, 513--565 (2012; Zbl 1279.35094) Full Text: DOI arXiv