A direct method for nonlinear ill-posed problems. (English) Zbl 1453.65125

Author’s abstract: We propose a direct method for solving nonlinear ill-posed problems in Banach-spaces. The method is based on a stable inversion formula we explicitly compute by applying techniques for analytic functions. Furthermore, we investigate the convergence and stability of the method and prove that the derived noniterative algorithm is a regularization. The inversion formula provides a systematic sensitivity analysis. The approach is applicable to a wide range of nonlinear ill-posed problems. We test the algorithm on a nonlinear problem of travel-time inversion in seismic tomography. Numerical results illustrate the robustness and efficiency of the algorithm.


65J20 Numerical solutions of ill-posed problems in abstract spaces; regularization
47J20 Variational and other types of inequalities involving nonlinear operators (general)
65J15 Numerical solutions to equations with nonlinear operators
86A15 Seismology (including tsunami modeling), earthquakes


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