Talk by Simon Hubmer, Johannes Kepler University Linz

Two-Point Gradient Methods for solving Nonlinear Ill-Posed Problems

Abstract

We present and analyse a class of gradient based iterative methods for solving nonlinear ill-posed problems which are inspired by Landweber iteration and Nesterov's acceleration scheme and promise to be good alternatives to second order methods. The usefulness of these methods is demonstrated on two numerical example problems based on a nonlinear Hammerstein operator and the nonlinear inverse problem of single photon emission computed tomography (SPECT).