A Note on Epsilon-Inflation

Abstract. The epsilon-inflation proved to be useful and necessary in many verification algorithms. Different definitions of an epsilon-inflation are possible, depending on the context. Recently, certain theoretical justifications and optimality results were proved for an epsilon-inflation without absolute term. In this note we show that in currently used interval iterations the epsilon-inflation without absolute term does not serve the purpose it is defined for. A new epsilon-inflation is proposed. Many verification algorithms for calculating an inclusion of the solution of a given problem use Banach’s or Brouwer’s Fixed Point theorem. The main point of those algorithms is to verify that a certain interval is mapped into itself or into its interior. We assume the reader is familiar with the fact that this self-mapping is the central part of many verification algorithms for systems of linear or nonlinear equations, algebraic eigenproblems, polynomial zeros and others. Re...

• Type: Journal
• Year: 1998
• Where: RC
• Authors: Siegfried M. Rump
• Keywords: Absolute Term, Interval Iteration, RC 1998, Verification Algorithms