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.
Mots-clés : 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://archive.numdam.org/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://archive.numdam.org/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://archive.numdam.org/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. http://archive.numdam.org/articles/10.1051/ita:2007006/
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