On Singular Interval Systems

We consider the interval iteration [x] k + 1 = [A] [x] k + [b] with ρ(|[A]|) ≤ 1 where |[A]| denotes the absolute value of the given interval matrix [A] . If |[A]| is irreducible we derive a necessary and sufficient criterion for the existence of the limit [x]* = [x]*([x]0) of each sequence ([x] k ) of interval iterates. In this way we generalize a well–known theorem of O. Mayer [6] on the above–mentioned iteration, and we are able to enclose solutions of certain singular systems (I – A) x = b with A ∈ [A] and degenerate interval vectors [b] ≡ b . Moreover, we give a connection between the convergence of ([x] k ) and the convergence of the powers of [A] .