10 papers
Row completion of polynomial and rational matrices II
Agurtzane Amparan, Itziar Baragaña, Silvia Marcaida +1
We study the row completion problem of polynomial and rational matrices with partial prescription of the structural data. The prescription of the complete structural data has been…
Polynomial and rational matrices with the invariant rational functions and the four sequences of minimal indices prescribed
Itziar Baragaña, Froilán M. Dopico, Silvia Marcaida +1
The complete eigenstructure, or structural data, of a rational matrix is comprised by its invariant rational functions, both finite and at infinity, which in turn determine…
Row completion of polynomial and rational matrices
Agurtzane Amparan, Itziar Baragaña, Silvia Marcaida +1
We characterize the existence of a polynomial (rational) matrix when its eigenstructure (complete structural data) and some of its rows are prescribed. For polynomial matrices, thi…
Row or column completion of polynomial matrices of given degree II
Agurtzane Amparan, Itziar Baragaña, Silvia Marcaida +1
The row (column) completion problem of polynomial matrices of given degree with prescribed eigenstructure has been studied in \cite{AmBaMaRo23}, where several results of prescripti…
Row or column completion of polynomial matrices of given degree
A. Amparan, I. Baragaña, S. Marcaida +1
We solve the problem of characterizing the existence of a polynomial matrix of fixed degree when its eigenstructure (or part of it) and some of its rows (columns) are prescribed. M…
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…
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…
On minimal bases and indices of rational matrices and their linearizations
Agurtzane Amparan, Froilan M. Dopico, Silvia Marcaida +1
A complete theory of the relationship between the minimal bases and indices of rational matrices and those of their strong linearizations is presented. Such theory is based on esta…
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…