Publisher DOI: 10.1016/j.laa.2009.10.014
Title: Detecting hyperbolic and definite matrix polynomials
Language: English
Authors: Niendorf, Vasco 
Voß, Heinrich 
Keywords: Definite matrix polynomial;Hyperbolic;Matrix polynomial;Minmax characterization;Overdamped;Quadratic eigenvalue problem;Safeguarded iteration
Issue Date: 17-Nov-2009
Publisher: American Elsevier Publ.
Source: Linear Algebra and Its Applications 4 (432): 1017-1035 (2010)
Abstract (english): 
Hyperbolic or more generally definite matrix polynomials are important classes of Hermitian matrix polynomials. They allow for a definite linearization and can therefore be solved by a standard algorithm for Hermitian matrices. They have only real eigenvalues which can be characterized as minmax and maxmin values of Rayleigh functionals, but there is no easy way to test if a given polynomial is hyperbolic or definite or not. Taking advantage of the safeguarded iteration which converges globally and monotonically to extreme eigenvalues we obtain an efficient algorithm that identifies hyperbolic or definite polynomials and enables the transformation to an equivalent definite linear pencil. Numerical examples demonstrate the efficiency of the approach. © 2009 Elsevier Inc. All rights reserved.
ISSN: 0024-3795
Institute: Mathematik E-10 
Numerische Simulation E-10 (H) 
Document Type: Article
Journal: Linear algebra and its applications 
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