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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…
Perturbation theory of transfer function matrices
Vanni Noferini, Lauri Nyman, Javier Pérez +1
Zeros of rational transfer function matrices are the eigenvalues of associated polynomial system matrices , under minimality conditions. In this paper we define a stru…
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…
Diagonal scalings for the eigenstructure of arbitrary pencils
Froilán M. Dopico, María C. Quintana, Paul Van Dooren
In this paper we show how to construct diagonal scalings for arbitrary matrix pencils , in which both and are complex matrices (square or nonsquare). The goal of such…
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…
Local Linearizations of Rational Matrices with Application to Rational Approximations of Nonlinear Eigenvalue Problems
Froilán M. Dopico, Silvia Marcaida, María C. Quintana +1
This paper presents a definition for local linearizations of rational matrices and studies their properties. This definition allows us to introduce matrix pencils associated to a r…
Strong linearizations of rational matrices with polynomial part expressed in an orthogonal basis
Froilán M. Dopico, Silvia Marcaida, María C. Quintana
We construct a new family of strong linearizations of rational matrices considering the polynomial part of them expressed in a basis that satisfies a three term recurrence relation…