10 citations · 24 across the 22 of their papers we have counts for
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A Riemannian optimization method to compute the nearest singular pencil
Froilán Dopico, Vanni Noferini, Lauri Nyman
Given a square pencil , where and are complex (resp. real) matrices, we consider the problem of finding the singular complex (resp. real) pencil nearest…
The vector space of pencils for singular matrix polynomials
Froilán Dopico, Vanni Noferini
Given a possibly singular matrix polynomial , we study how the eigenvalues, eigenvectors, root polynomials, minimal indices, and minimal bases of the pencils in the vector sp…
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…
Generic eigenstructures of Hermitian pencils
Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico
We obtain the generic complete eigenstructures of complex Hermitian matrix pencils with rank at most (with ). To do this, we prove that the set of such pen…
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…
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…
Generic symmetric matrix polynomials with bounded rank and fixed odd grade
Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico
We determine the generic complete eigenstructures for complex symmetric matrix polynomials of odd grade and rank at most . More precisely, we show that the set…
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…
Conditioning and backward errors of eigenvalues of homogeneous matrix polynomials under Möbius transformations
Luis Miguel Anguas, María Isabel Bueno, Froilán M. Dopico
Möbius transformations have been used in numerical algorithms for computing eigenvalues and invariant subspaces of structured generalized and polynomial eigenvalue problems (PEPs).…
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…
A comparison of eigenvalue condition numbers for matrix polynomials
Luis Miguel Anguas, María Isabel Bueno, Froilán M. Dopico
In this paper, we consider the different eigenvalue condition numbers for matrix polynomials used in the literature and we compare them. One of these condition numbers is a general…
Block minimal bases -ifications of matrix polynomials
Froilán M. Dopico, Javier Pérez, Paul Van Dooren
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,…
Robustness and perturbations of minimal bases II: The case with given row degrees
Froilán M. Dopico, Paul Van Dooren
This paper studies generic and perturbation properties inside the linear space of polynomial matrices whose rows have degrees bounded by a given list $d_1, \ldots,…
Block Kronecker Linearizations of Matrix Polynomials and their Backward Errors
Froilán M. Dopico, Piers W. Lawrence, Javier Pérez +1
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 polynomia…
Conditioning and backward error of block-symmetric block-tridiagonal linearizations of matrix polynomials
M. I. Bueno, F. M. Dopico, S. Furtado +1
For each square matrix polynomial of odd degree, a block-symmetric block-tridiagonal pencil was introduced by Antoniou and Vologiannidis in 2004, and a…
A compact rational Krylov method for large-scale rational eigenvalue problems
Froilán M. Dopico, Javier González-Pizarro
In this work, we propose a new method, termed as R-CORK, for the numerical solution of large-scale rational eigenvalue problems, which is based on a linearization and on a compact…
Structured backward error analysis of linearized structured polynomial eigenvalue problems
Froilán M. Dopico, Javier Pérez, Paul Van Dooren
We introduce a new class of structured matrix polynomials, namely, the class of M_A-structured matrix polynomials, to provide a common framework for many classes of structured matr…
Generic matrix polynomials with fixed rank and fixed degree
Andrii Dmytryshyn, Froilán M. Dopico
The set of complex matrix polynomials of grade and (normal) rank at most in a complex dimensional space is studied. For…
Robustness and Perturbations of Minimal Bases
Paul Van Dooren, Froilán M. Dopico
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 comm…
A unified approach to Fiedler-like pencils via strong block minimal bases pencils
Maribel Bueno Cachadina, Froilán M. Dopico, Javier Pérez +2
The standard way of solving the polynomial eigenvalue problem associated with a matrix polynomial is to embed the matrix polynomial into a matrix pencil, transforming the problem i…