论文标题
块的完整等级线性化的理性矩阵
Block Full Rank Linearizations of Rational Matrices
论文作者
论文摘要
在[Dopico等人的[Dopico等人，局部线性矩阵的局部线性化中引入的块全等级铅笔，均应用于非线性特征值问题的合理近似，线性代数应用，2020年]允许我们获得有关ZEROS的本地信息，这些信息不是理性矩阵的零件。在本文中，我们将这些块全等级铅笔的结构扩展到构造有理矩阵的线性化，这些矩阵使我们能够在满足某些最小值条件时不仅在本地恢复有关零的信息，还可以恢复有关杆的信息。另外，将使用有理矩阵的度量概念来确定新块的全等级线性化的等级为无穷大的线性化。这个新的线性化家族很重要，因为它概括了，并包括在文献中构建的大多数理性矩阵中出现的结构。特别是，该理论将用于研究[P. Lietaert等人，已提交的非线性特征值问题的自动合理近似和线性化]。
Block full rank pencils introduced in [Dopico et al., Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems, Linear Algebra Appl., 2020] allow us to obtain local information about zeros that are not poles of rational matrices. In this paper we extend the structure of those block full rank pencils to construct linearizations of rational matrices that allow us to recover locally not only information about zeros but also about poles, whenever certain minimality conditions are satisfied. In addition, the notion of degree of a rational matrix will be used to determine the grade of the new block full rank linearizations as linearizations at infinity. This new family of linearizations is important as it generalizes and includes the structures appearing in most of the linearizations for rational matrices constructed in the literature. In particular, this theory will be applied to study the structure and the properties of the linearizations in [P. Lietaert et al., Automatic rational approximation and linearization of nonlinear eigenvalue problems, submitted].
