Linear Interval Equations: Midpoint Preconditioning May Produce a 100% Overestimation for Arbitrarily Narrow Data Even in Case <Emphasis Type="Italic">n</Emphasis> = 4

We construct a linear interval system Ax = b with a 4 × 4 interval matrix whose all proper interval coefficients (there are also some noninterval ones) are of the form –, ]. It is proved that for each > 0, the interval hull and interval hull of the midpoint preconditioned system satisfy and , hence midpoint preconditioning produces a 100% overestimation of independently of in this case. The example was obtained as a result of an extensive MATLAB search.