1 citations · 1 across the 6 of their papers we have counts for
13 papers
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…
On bundles of matrix pencils under strict equivalence
Fernando De Terán, Froilán M. Dopico
Bundles of matrix pencils (under strict equivalence) are sets of pencils having the same Kronecker canonical form, up to the eigenvalues (namely, they are an infinite union of orbi…
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…