We introduce a new family of strong linearizations of matrix polynomials—which we call
“block Kronecker pencils”—and perform a backward stability analysis of complete …

This paper defines for the first time strong linearizations of arbitrary rational matrices, studies
in depth properties and characterizations of such linear matrix pencils, and develops …

We present a framework for the construction of linearizations for scalar and matrix
polynomials based on dual bases which, in the case of orthogonal polynomials, can be …

The standard way of solving the polynomial eigenvalue problem associated with a matrix
polynomial is to embed the matrix coefficients of the polynomial into a matrix pencil …

Regular and singular matrix polynomials P (λ)=∑ i= 0 k P i ϕ i (λ), P i∈ R n× n given in an
orthogonal basis ϕ 0 (λ), ϕ 1 (λ),…, ϕ k (λ) are considered. Following the ideas in [9], the …

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 …

In this paper, we introduce a new family of equations for matrix pencils that may be utilized
for the construction of strong linearizations for any square or rectangular matrix polynomial …

The standard way of solving a polynomial eigenvalue problem associated with a matrix
polynomial starts by embedding the matrix coefficients of the polynomial into a matrix pencil …

We describe a generalization of the compact rational Krylov (CORK) methods for polynomial
and rational eigenvalue problems that usually, but not necessarily, come from polynomial or …

Polynomial minimal bases of rational vector subspaces are a classical concept that plays an
important role in control theory, linear systems theory, and coding theory. It is a common …