In this paper we compare (augmented) GMRES-type methods and (augmented) CGNE methods. The numerical results show that the CGNE method is more robust and is suitable for ill-posed problems with a much higher degree of ill-posedness. GMRES-type methods only yield useful results for very moderate ill-posed problems.

On this talk we report on a joint work with Prof. B.Kaltenbacher on Levenberg-Marquardt type methods for solving nonlinear ill-posed operator equations in Hilbert spaces.

Moreover, we also discuss some recent research results on this iterative method.

In this talk a short introduction into to work of a mathematician at an insurance company will be given. Starting with the one and only necessary equation for insurance mathematics, over working as data analyst, or in marketing, we will end with the work of a mathematician in IT-department.