RAIRO-Theor. Inf. Appl.
Volume 41, Number 1, January-March 2007Real Numbers
|Page(s)||45 - 56|
|Published online||24 April 2007|
Real and complex pseudozero sets for polynomials with applications
Laboratoire LIP6, département Calcul scientifique, université Pierre et Marie Curie, 4 place Jussieu, F-75252, Paris Cedex 05, France; email@example.com
2 DALI Project, Laboratory LP2A, université de Perpignan, 52, avenue Paul Alduy, 66860 Perpignan Cedex, France; firstname.lastname@example.org
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.
Mathematics Subject Classification: 65F35 / 68W30
Key words: Polynomial root / pseudozero set / uncertainty / perturbation / stability.
© EDP Sciences, 2007
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.