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Real and complex pseudozero setsfor polynomials with applications

Published online by Cambridge University Press:  24 April 2007

Stef Graillat and
Philippe Langlois
Stef Graillat
Affiliation:
Laboratoire LIP6, département Calcul scientifique, université Pierre et Marie Curie, 4 place Jussieu, F-75252, Paris Cedex 05, France; stef.graillat@lip6.fr
Philippe Langlois
Affiliation:
DALI Project, Laboratory LP2A, université de Perpignan, 52, avenue Paul Alduy, 66860 Perpignan Cedex, France; langlois@univ-perp.fr
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Abstract

Pseudozeros are useful to describe how perturbations of polynomialcoefficients affect its zeros. We compare two types of pseudozerosets: 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 beenintensively studied while the second one – real perturbations of a realpolynomial – seems to have received little attention. We present a computable formula for the real pseudozero set and acomparison between these two pseudozero sets. We conclude that thecomplex pseudozero sets have to be preferred except when the perturbedreal polynomials admit non-real zeros. We also give some applicationsof pseudozero set in control theory.

Keywords

Polynomial rootpseudozero setuncertaintyperturbationstability.

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Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 41 , Issue 1: Real Numbers , January 2007, pp. 45 - 56
Copyright
© EDP Sciences, 2007

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