Expansion systems

Abstract

In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic properties of expansion systems, and also study criteria for convergence. Further, we introduce the notion of isomorphisms between expansion systems. In the appendix, we discuss another class of expansion systems, which we call approximation systems. Many claims of convergence in this appendix, remain to be proven.