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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.
Keywords: polynomial root, pseudozero set, uncertainty, perturbation, stability
@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},
pages = {45--56},
publisher = {EDP-Sciences},
volume = {41},
number = {1},
year = {2007},
doi = {10.1051/ita:2007006},
mrnumber = {2330042},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/ita:2007006/}
}
TY - JOUR AU - Graillat, Stef AU - Langlois, Philippe TI - Real and complex pseudozero sets for polynomials with applications JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2007 SP - 45 EP - 56 VL - 41 IS - 1 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/ita:2007006/ DO - 10.1051/ita:2007006 LA - en ID - ITA_2007__41_1_45_0 ER -
%0 Journal Article %A Graillat, Stef %A Langlois, Philippe %T Real and complex pseudozero sets for polynomials with applications %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2007 %P 45-56 %V 41 %N 1 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/ita:2007006/ %R 10.1051/ita:2007006 %G en %F 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) no. 1, pp. 45-56. doi: 10.1051/ita:2007006
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