Convergence of the Arnoldi Process when applied to the Picard-Lindelöf Iteration Operator

Abstract

In this paper the iteration operator corresponding to the Picard-Lindelöf iteration is considered as a model case in order to investigate the convergence theory of the Arnoldi process. We ask whether it is possible to use a theorem by Nevanlinna and Vainikko to obtain the spectrum of the local operator. In the cases considered here the answer is no.