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.

中文翻译：

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具有公共零空间的最近结构化矩阵三元组的计算

我们研究了计算奇异点距离、最近高指数问题的距离以及具有耗散哈密顿结构的线性微分代数系统 (DAE) 的不稳定距离的计算方法。虽然对于一般的非结构化 DAE，这些距离的表征非常困难，而且是部分开放的，但最近已经表明，对于耗散哈密顿系统和相关的矩阵铅笔，存在明确的表征。我们将使用这些特征来开发计算方法，通过遵循微分方程流的方法来计算这些距离，这些方法会收敛到破坏规律性、指数 1 或稳定性属性的最小扰动。