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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" ε 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.doi:10.1137/s0036142996299423 fatcat:vvvvwohw7jap7nhnjabdkekvxi