A bisection method is used to compute lower and upper bounds on the distance from a quadratic matrix polynomial to the set of quadratic matrix polynomials having an eigenvalue on the imaginary axis. Each bisection step requires to check whether an even quadratic matrix polynomial has a purely imaginary eigenvalue. First, an upper bound is obtained using Frobenius-type linearizations. It takes into account rounding errors but does not use the even structure. Then, lower and upper bounds are obtained by reducing the quadratic matrix polynomial to a linear palindromic pencil. The bounds obtained this way also take into account rounding errors. Numerical illustrations are presented.

中文翻译：

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计算二次矩阵多项式到连续时间不稳定性的距离

二分法用于计算从二次矩阵多项式到在虚轴上具有特征值的二次矩阵多项式集合的距离的下限和上限。每个二分步骤都需要检查偶二次矩阵多项式是否具有纯虚特征值。首先，使用 Frobenius 型线性化获得上限。它考虑了舍入误差，但不使用偶数结构。然后，通过将二次矩阵多项式化简为线性回文铅笔来获得上下界。以这种方式获得的边界也考虑了舍入误差。给出了数字插图。