A direct method for nonlinear ill-posed problems. (29th December 2017)

• Record Type: Journal Article
• Authors: Lakhal, A
• Is Part Of: Inverse problems. Volume 34:Number 2(2018:Feb.)
• Publication Date: 2017-12-29
• Subjects: nonlinear ill-posed problems -- regularization -- sensitivity -- nonlinear seismic tomography; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aa91e0
• Languages: English
• ISSNs: 0266-5611

Abstract

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.