8 papers
Para-Hermitian rational matrices
Froilán Dopico, Vanni Noferini, María C. Quintana +1
In this paper we study para-Hermitian rational matrices and the associated structured rational eigenvalue problem (REP). Para-Hermitian rational matrices are square rational matric…
Linearizations of matrix polynomials viewed as Rosenbrock's system matrices
Froilán M. Dopico, Silvia Marcaida, María C. Quintana +1
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…
Strongly minimal self-conjugate linearizations for polynomial and rational matrices
Froilán M. Dopico, María C. Quintana, Paul Van Dooren
We prove that we can always construct strongly minimal linearizations of an arbitrary rational matrix from its Laurent expansion around the point at infinity, which happens to be t…
Structural backward stability in rational eigenvalue problems solved via block Kronecker linearizations
Froilán M. Dopico, María C. Quintana, Paul Van Dooren
We study the backward stability of running a backward stable eigenstructure solver on a pencil that is a strong linearization of a rational matrix expressed in the fo…
Block Full Rank Linearizations of Rational Matrices
Froilán M. Dopico, Silvia Marcaida, María C. Quintana +1
Block full rank pencils introduced in [Dopico et al., Local linearizations of rational matrices with application to rational approximations of nonlinear eigenvalue problems, Linear…
Linearizations of rational matrices from general representations
Javier Pérez, María C. Quintana
We construct a new family of linearizations of rational matrices written in the general form , where , , and are poly…