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.

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.

DOI : https://doi.org/10.1051/ita:2007006
Classification : 65F35,  68W30
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://www.numdam.org/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) no. 1, pp. 45-56. doi : 10.1051/ita:2007006. http://www.numdam.org/item/ITA_2007__41_1_45_0/

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