F. Dopico

Publications
Influence

Fiedler Companion Linearizations and the Recovery of Minimal Indices

F. Terán, F. Dopico, D. S. Mackey
Computer Science, Mathematics
SIAM J. Matrix Anal. Appl.
2010

A standard way of dealing with a matrix polynomial $P(\lambda)$ is to convert it into an equivalent matrix pencil—a process known as linearization. Expand

Spectral equivalence of matrix polynomials and the index sum theorem

F. Terán, F. Dopico, D. S. Mackey
Mathematics
15 October 2014

Abstract The concept of linearization is fundamental for theory, applications, and spectral computations related to matrix polynomials. However, recent research on several important classes of… Expand

Block Kronecker linearizations of matrix polynomials and their backward errors

F. Dopico, P. Lawrence, J. Pérez, P. Dooren
Mathematics, Computer Science
Numerische Mathematik
16 July 2017

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 polynomial eigenproblems. Expand

Implicit standard Jacobi gives high relative accuracy

F. Dopico, P. Koev, J. M. Molera
Mathematics, Computer Science
Numerische Mathematik
29 September 2009

We prove that the Jacobi algorithm applied implicitly on a decomposition A = XDXT of the symmetric matrix A, where D is diagonal, and X is well conditioned, computes all eigenvalues of A to high relative accuracy. Expand

Low Rank Perturbation of Jordan Structure

J. Moro, F. Dopico
Mathematics, Computer Science
SIAM J. Matrix Anal. Appl.
1 February 2003

We show that for most matrices B satisfying ${\rm rank}\,(B)\leq g$, the Jordan blocks of A+B with eigenvalue $\lambda_0$ are just the smallest Jordan blocks in the Jordan canonical form of A, while the rest remain unchanged. Expand

Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices

F. Dopico, J. Moro, J. M. Molera
Mathematics
15 April 2000

We present a Weyl-type relative bound for eigenvalues of Hermitian perturbations A+E of (not necessarily definite) Hermitian matrices A. This bound, given in function of the quantity… Expand

Complementary bases in symplectic matrices and a proof that their determinant is one

F. Dopico, C. Johnson
Mathematics
1 December 2006

New results on the patterns of linearly independent rows and columns among the blocks of a symplectic matrix are presented. These results are combined with the block structure of the inverse of a… Expand

Accurate solution of structured linear systems via rank-revealing decompositions

F. Dopico, J. M. Molera
Mathematics
1 July 2012

Linear systems of equations Ax = b, where the matrix A has some particular structure, arise frequently in applications. Very often structured matrices have huge condition numbers κ(A) = ‖A−1‖‖A‖ and,… Expand

Matrix Polynomials with Completely Prescribed Eigenstructure

F. Terán, F. Dopico, P. Dooren
Mathematics, Computer Science
SIAM J. Matrix Anal. Appl.
24 March 2015

We present necessary and sufficient conditions for the existence of a matrix polynomial when its degree, its finite and infinite elementary divisors, and its left and right minimal indices are prescribed. Expand

Large vector spaces of block-symmetric strong linearizations of matrix polynomials

M. Bueno, F. Dopico, S. Furtado, M. Rychnovsky
Mathematics
15 July 2015

Abstract Given a matrix polynomial P ( λ ) = ∑ i = 0 k λ i A i of degree k , where A i are n × n matrices with entries in a field F , the development of linearizations of P ( λ ) that preserve… Expand

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