论文标题
矩阵多项式的线性化，被视为Rosenbrock的系统矩阵
Linearizations of matrix polynomials viewed as Rosenbrock's system matrices
论文作者
论文摘要
解决多项式特征值问题（PEP）的一种众所周知的方法是通过线性化。也就是说，将PEP转换为具有相同光谱信息的广义线性特征值问题，并使用文献中一些特征值算法解决了此类线性问题。基质多项式的线性化通常是使用单型转换定义的。在本文中，我们建立了Gohberg，Lancaster和Rodman引入的矩阵多项式的线性化标准定义与Rosenbrock引入的多项式系统矩阵的概念之间的连接。该连接提供了新技术，以表明矩阵铅笔是PEP中出现的相应基质多项式的线性化。
A well known method to solve the Polynomial Eigenvalue Problem (PEP) is via linearization. That is, transforming the PEP into a generalized linear eigenvalue problem with the same spectral information and solving such linear problem with some of the eigenvalue algorithms available in the literature. Linearizations of matrix polynomials are usually defined using unimodular transformations. In this paper we establish a connection between the standard definition of linearization for matrix polynomials introduced by Gohberg, Lancaster and Rodman and the notion of polynomial system matrix introduced by Rosenbrock. This connection gives new techniques to show that a matrix pencil is a linearization of the corresponding matrix polynomial arising in a PEP.
