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Real and complex pseudozero sets for polynomials with applications

Stef Graillat 1 Philippe Langlois 2
1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
2 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : Pseudozeros are useful to describe how perturbations of polynomial coefficients affect its zeros. We compare two types of pseudozero sets: the complex and the real pseudozero sets. These sets differ with respect to the type of perturbations. The first set – complex perturbations of a complex polynomial – has been intensively studied while the second one – real perturbations of a real polynomial – seems to have received little attention. We present a computable formula for the real pseudozero set and a comparison between these two pseudozero sets. We conclude that the complex pseudozero sets have to be preferred except when the perturbed real polynomials admit non-real zeros. We also give some applications of pseudozero set in control theory.
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Submitted on : Tuesday, April 28, 2015 - 2:41:26 PM
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Stef Graillat, Philippe Langlois. Real and complex pseudozero sets for polynomials with applications. RAIRO - Theoretical Informatics and Applications (RAIRO: ITA), EDP Sciences, 2007, 41 (1), pp.45-56. ⟨10.1051/ita:2007006⟩. ⟨hal-01146488⟩



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