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.
Reviewer: Xiaolong Qin (Chengdu)
MSC:
| 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 |
Software:
KAIRUAINReferences:
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