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This paper proposes a new interval-based contractor for nonlinear equationswhich is minimal when dealing with narrow boxes. The method is based on thecentered form classically used by interval algorithms combined with a GaussJordan band diagonalization preconditioning. As an illustration in stabilityanalysis, we propose to compute the set of all parameters of a characteristicfunction of a linear dynamical system which have at least one zero in theimaginary axis. Our approach is able compute a guaranteed and accurateenclosure of the solution set faster than existing approaches.

Asymptotically minimal contractors based on the centered form;Application to the stability analysis of linear systems