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.