Enclosing solutions of linear equations

It is shown that Rump's method for enclosing solutions of linear equations can be reformulated in an interval-free form and that the underlying inclusion result can be proved by elementary means without using Brouwer's fixed-point theorem. A sufficient condition on Rump's "inflation parameter" epsilon is given under which finite termination occurs. Also, a more general modified algorithm is studied for which the number of iterations can be expressed by an explicit formula.