The largest eigenvalue of nonnegative tensors

Abstract

In this thesis we study the methods for finding the largest eigenvalue of tensors. In particular, we study the convergence of the methods and show that the method for rectangular tensors is Q-linear convergence under weak irreducibility condition. We further generalise the method to nonnegative polynomial eigenvalue problems. We prove that this method is convergent for nonhomogeneous irreducible nonnegative polynomials. Then, we apply this method to solve nonnegative polynomial optimization problems with spherical constraints.