Enclosing Solutions of Singular Interval Systems Iteratively

Richardson splitting applied to a consistent system of linear equations Cx = b with a singular matrix C yields to an iterative method x^k+1 = Ax^k + b where A has the eigenvalue one. It is known that each sequence of iterates is convergent to a vector x^* = x^* (x⁰) if and only if A is semi-convergent. In order to enclose such vectors we consider the corresponding interval iteration with (|A]|) = 1 where |A]| denotes the absolute value of the interval matrix A]. If |A]| is irreducible we derive a necessary and sufficient criterion for the existence of a limit of each sequence of interval iterates. We describe the shape of and give a connection between the convergence of ( ) and the convergence of the powers of A].Dedicated to Professor G. Mae on the occasion of his 65^th birthday