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.
@article{ITA_2007__41_1_45_0,
author = {Graillat, Stef and Langlois, Philippe},
title = {Real and complex pseudozero sets for polynomials with applications},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {41},
year = {2007},
pages = {45-56},
doi = {10.1051/ita:2007006},
mrnumber = {2330042},
zbl = {pre05238553},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2007__41_1_45_0}
}
Graillat, Stef; Langlois, Philippe. Real and complex pseudozero sets for polynomials with applications. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 41 (2007) pp. 45-56. doi : 10.1051/ita:2007006. http://gdmltest.u-ga.fr/item/ITA_2007__41_1_45_0/
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