  This paper proposes a new interval-based contractor for nonlinear equations
which is minimal when dealing with narrow boxes. The method is based on the
centered form classically used by interval algorithms combined with a Gauss
Jordan band diagonalization preconditioning. As an illustration in stability
analysis, we propose to compute the set of all parameters of a characteristic
function of a linear dynamical system which have at least one zero in the
imaginary axis. Our approach is able compute a guaranteed and accurate
enclosure of the solution set faster than existing approaches.
