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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

95 12- PDF

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

87 11- PDF

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

66 5- PDF

Matrix Polynomials with Completely Prescribed Eigenstructure

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

TLDR

39 3- PDF

The solution of the equation XA + AXT = 0 and its application to the theory of orbits

- F. Terán, F. M. Dopico
- Mathematics
- 2011

Abstract describe how to find the general solution of the matrix equation XA + AX T = 0 , with A ∈ C n × n , which allows us to determine the dimension of its solution space. This result has… Expand

43 3- PDF

New bounds for roots of polynomials based on Fiedler companion matrices

- F. Terán, F. M. Dopico, J. Pérez
- Mathematics
- 15 June 2014

Abstract Several matrix norms of the classical Frobenius companion matrices of a monic polynomial p ( z ) have been used in the literature to obtain simple lower and upper bounds on the absolute… Expand

9 3- PDF

First order spectral perturbation theory of square singular matrix pencils

- F. Terán, F. M. Dopico, J. Moro
- Mathematics
- 15 July 2008

Abstract Let H ( λ ) = A 0 + λ A 1 be a square singular matrix pencil, and let λ 0 ∈ C be an eventually multiple eigenvalue of H ( λ ) . It is known that arbitrarily small perturbations of H ( λ )… Expand

24 2- PDF

Fiedler companion linearizations for rectangular matrix polynomials

- F. Terán, F. M. Dopico, D. S. Mackey
- Mathematics
- 1 August 2012

The development of new classes of linearizations of square matrix polynomials that generalize the classical first and second Frobenius companion forms has attracted much attention in the last decade.… Expand

48 2- PDF

Backward stability of polynomial root-finding using Fiedler companion matrices

- F. Terán, F. M. Dopico, J. Pérez
- Mathematics
- 28 July 2014

Computing roots of scalar polynomials as the eigenvalues of Frobenius companion matrices using backward stable eigenvalue algorithms is a classical approach. The introduction of new families of… Expand

18 2- PDF

Low Rank Perturbation of Weierstrass Structure

- F. Terán, F. M. Dopico, J. Moro
- Mathematics, Computer Science
- SIAM J. Matrix Anal. Appl.
- 1 May 2008

TLDR

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