On projective Landweber-Kaczmarz methods for solving systems of nonlinear ill-posed equations

Abstract

In this article we combine the projective Landweber method, recently proposed by the authors, with Kaczmarz's method for solving systems of non-linear ill-posed equations. The underlying assumption used in this work is the tangential cone condition. We show that the proposed iteration is a convergent regularization method. Numerical tests are presented for a non-linear inverse problem related to the Dirichlet-to-Neumann map, indicating a superior performance of the proposed method when compared with other well established iterations. Our preliminary investigation indicates that the resulting iteration is a promising alternative for computing stable solutions of large scale systems of nonlinear ill-posed equations.

22 pages, 3 figures

References in corpus (5)

• Regularization of systems of nonlinear ill-posed equations: I. Convergence Analysis
• Regularization of systems of nonlinear ill-posed equations: II. Applications
• On Levenberg-Marquardt-Kaczmarz iterative methods for solving systems of nonlinear ill-posed equations
• On inverse problems for semiconductor equations
• Semiconductors and Dirichlet-to-Neumann maps