论文标题
使用Julia计算多项式和有理矩阵的Kronecker结构
On Computing the Kronecker Structure of Polynomial and Rational Matrices using Julia
论文作者
论文摘要
在本文中，我们讨论了数学背景和计算方面，这些方面的基础是julia函数集合中的矩阵函数包装，以确定多项式和有理矩阵的结构属性。我们主要集中于有限和无限光谱结构（例如特征值，零，杆，杆）以及左右单数结构（例如，克罗内克指数）的计算，这些结构在许多问题的解决方案的结构中起着基本作用，这些结构涉及多个涉及多元素和理性矩阵的解决方案的结构。基本分析工具是使用数值可靠的算法确定线性基质铅笔的Kronecker结构，该算法与多项式和有理矩阵的几种线性化技术一起使用。认为具有所有相关结构特征的多项式和理性矩阵的示例被认为是为了说明主要的数学概念和实施工具的能力。
In this paper we discuss the mathematical background and the computational aspects which underly the implementation of a collection of Julia functions in the MatrixPencils package for the determination of structural properties of polynomial and rational matrices. We primarily focus on the computation of the finite and infinite spectral structures (e.g., eigenvalues, zeros, poles) as well as the left and right singular structures (e.g., Kronecker indices), which play a fundamental role in the structure of the solution of many problems involving polynomial and rational matrices. The basic analysis tool is the determination of the Kronecker structure of linear matrix pencils using numerically reliable algorithms, which is used in conjunction with several linearization techniques of polynomial and rational matrices. Examples of polynomial and rational matrices, which exhibit all relevant structural features, are considered to illustrate the main mathematical concepts and the capabilities of implemented tools.
