Comparison Theorems for Iterative Methods Based on Strong Splittings

By means of strong splittings of an $n \times n$ interval M-matrix $\mathcal {A}$ one can construct iterative methods to enclose the solution set $\{ x\} : = \{ x|Ax = b,A \in A,b \in \mathfrak{b}\} $, where $\mathfrak{b}$ is an interval vector and $x \in \mathbb{R}^n $. We derive comparison theorems for an upper bound of the asymptotic convergence factor and for the fixpoints resulting from those methods.