In this article we combine the projective Landweber method, recently proposed
by the authors, with Kaczmarz's method for solving systems of non-linear
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.