We study computational methods for computing the distance to singularity, the distance to the nearest high index problem, and the distance to instability for linear differential-algebraic systems (DAEs) with dissipative Hamiltonian structure. While for general unstructured DAEs the characterization of these distances is very difficult, and partially open, it has been recently shown that for dissipative Hamiltonian systems and related matrix pencils there exist explicit characterizations. We will use these characterizations for the development of computational methods to compute these distances via methods that follow the flow of a differential equation converging to the smallest perturbation that destroys the property of regularity, index one or stability.

翻译：我们研究计算距离至奇点的计算方法,距离至最近的高指数问题,以及线性差分位数系统(DAEs)与分布式汉密尔顿结构的不稳定的距离。虽然对于一般非结构化的DAE来说,这些距离的定性非常困难,而且部分开放,但最近已经表明,对于消散式汉密尔顿系统和相关的矩阵铅笔来说,存在着明确的特征。我们将利用这些特征来发展计算方法,以便按照差分方程趋同到破坏正常性、指数1或稳定性的最小扰动状态的方法来计算这些距离。