标题： 通过预处理阶段计算常规线性时变微分代数方程的标准规范形式 显示英文标题

标题： Computing standard canonical forms of regular linear time varying DAEs via a preliminary stage

摘要： 对于常规的线性时不变微分代数方程（DAE），相应的矩阵束是常规的，计算标准规范形式是众所周知的。 尽管研究具有时变系数的线性DAE更为复杂，但其与检查时变矩阵函数对的情况类似。 我们展示如何在前期阶段找到矩阵函数对的合适块结构，从而使得计算线性时变DAE的标准规范形式（SCF）成为可能。 从这一前期阶段开始，迭代过程可以生成一个SCF。 由于涉及矩阵的幂零性，该迭代过程在有限步骤内终止。 相应的变换矩阵函数可以系统地提供，这也会导致与原始DAE相关的规范子空间和投影算子的新表示。 我们演示了如何将结构化规范形式转换到这一前期阶段，并讨论了一些示例，这些结构化规范形式来自可解性和奇异框架以及应用中的一些Hessenberg形式DAE。 显示英文摘要

摘要： For regular linear time-invariant DAEs the corresponding matrix pencil is regular and the computation of a standard canonical form is well-understood. Although the investigation of linear DAEs with time-varying coefficients is more complex, it is analogously related to the examination of pairs of time-dependent matrix functions. We show how the computation of a standard canonical form (SCF) for linear time-varying DAEs becomes possible if a suitable block structure of the pair of matrix functions is found in a preliminary stage. Starting from this preliminary stage, an iterative process delivers an SCF. This iteration terminates in finitely many steps due to the nilpotency of an involved matrix. The corresponding transformation matrix functions can be provided systematically, which leads also to new representations of the canonical subspaces and projectors related to the original DAE. We demonstrate how the structured canonical forms resulting in the tractability and strangeness frameworks and some DAEs in Hessenberg form from applications can be transformed into this preliminary stage and discuss some examples.