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.

翻译：本文提出了一种新的基于区间的非线性方程收缩算子，该算子在处理窄箱时具有最小性。该方法基于区间算法中经典使用的中心形式，并结合了高斯-约当带状对角化预处理。作为稳定性分析中的示例，我们提出计算线性动力系统特征函数中所有在虚轴上至少存在一个零点的参数集合。我们的方法能够比现有方法更快地计算出解集的带保证且精确的包络。