Epsilon-inflation in verification algorithms

Epsilon-inflation is often used in verification numerics to find an interval vector [x]∈ such that some interval function [ƒ] maps [x]∈ into itself. We recall algorithms which use epsilon-inflation to verify this subset property [ƒ] ([x]ϵ) ⊆ [x]ϵ, and we derive criteria which guarantee that already finitely many inflation steps are sufficient to prove it. These criteria require [ƒ] to be a P-contraction. We recall results on P-contractions, and we derive rules to verify them. We also introduce local P-contractions, and we use this concept to guarantee again the subset property above when using epsilon-inflation.