10 citations · 24 across the 22 of their papers we have counts for
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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).…
Generic symmetric matrix pencils with bounded rank
Fernando De Terán, Andrii Dmytryshyn, Froilán M. Dopico
We show that the set of complex symmetric matrix pencils of rank at most is the union of the closures of sets of matrix pencils with some,…
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,…