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Fiedler Companion Linearizations and the Recovery of Minimal Indices

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

TLDR

Spectral equivalence of matrix polynomials and the index sum theorem

- F. Terán, F. M. 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. M. Dopico, Piers W. Lawrence, J. Pérez, P. Dooren
- Mathematics, Computer Science
- Numerische Mathematik
- 16 July 2017

TLDR

LINEARIZATIONS OF SINGULAR MATRIX POLYNOMIALS AND THE RECOVERY OF MINIMAL INDICES

- F. Terán, F. M. Dopico, D. S. Mackey
- Mathematics
- 26 March 2009

A standard way of dealing with a regular matrix polynomial P (λ) is to convert it into an equivalent matrix pencil - a process known as linearization. Two vector spaces of pencils L1(P ) and L2(P )… Expand

Weyl-type relative perturbation bounds for eigensystems of Hermitian matrices

- F. M. Dopico, J. Moro, Juan 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

Implicit standard Jacobi gives high relative accuracy

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

TLDR

Low Rank Perturbation of Jordan Structure

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

TLDR

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

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

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