We start by introducing a new class of structured matrix polynomials, namely, the class of
$\mathbf {M} _A $-structured matrix polynomials, to provide a common framework for many …

We show how to construct linearizations of matrix polynomials za (z) d 0+ c 0, a (z) b (z), a
(z)+ b (z)(when deg (b (z))< deg (a (z))), and za (z) d 0 b (z)+ c 0 from linearizations of the …

In this paper we associate a class of Hurwitz matrix polynomials with Stieltjes positive
definite matrix sequences. This connection leads to an extension of two classical criteria of …

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 …

In the framework of Polynomial Eigenvalue Problems, most of the matrix polynomials arising
in applications are structured polynomials (namely (skew-) symmetric,(skew-) Hermitian,(anti …

We construct a new family of linearizations of rational matrices R (λ) written in the general
form R (λ)= D (λ)+ C (λ) A (λ)− 1 B (λ), where D (λ), C (λ), B (λ) and A (λ) are polynomial …

In the last decade, there has been a continued effort to produce families of strong
linearizations of a matrix polynomial $ P (\lambda) $, regular and singular, with good …

One strategy to solve a nonlinear eigenvalue problem $ T (\lambda) x= 0$ is to solve a
polynomial eigenvalue problem (PEP) $ P (\lambda) x= 0$ that approximates the original …

2023 World Scientific Publishing Company Page 54 2023 World Scientific Publishing Company
https://doi. org/10.1142/9789811261572_0003 Chapter 3 Upper and Lower Semicontinuous …

Matrix polynomials are a prominent tool in the representation and study of systems of
differential or difference equations. Systems of such equations can be described via …