Real and complex pseudozero sets for polynomials with applications
Stef Graillat; Philippe Langlois
RAIRO - Theoretical Informatics and Applications (2007)
- Volume: 41, Issue: 1, page 45-56
- ISSN: 0988-3754
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topGraillat, Stef, and Langlois, Philippe. "Real and complex pseudozero sets for polynomials with applications." RAIRO - Theoretical Informatics and Applications 41.1 (2007): 45-56. <http://eudml.org/doc/250033>.
@article{Graillat2007,
abstract = {
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.
},
author = {Graillat, Stef, Langlois, Philippe},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Polynomial root; pseudozero set; uncertainty; perturbation; stability.; pseudozero of of polynomial; root perturbation; computational stability; control theory},
language = {eng},
month = {4},
number = {1},
pages = {45-56},
publisher = {EDP Sciences},
title = {Real and complex pseudozero sets for polynomials with applications},
url = {http://eudml.org/doc/250033},
volume = {41},
year = {2007},
}
TY - JOUR
AU - Graillat, Stef
AU - Langlois, Philippe
TI - Real and complex pseudozero sets for polynomials with applications
JO - RAIRO - Theoretical Informatics and Applications
DA - 2007/4//
PB - EDP Sciences
VL - 41
IS - 1
SP - 45
EP - 56
AB -
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.
LA - eng
KW - Polynomial root; pseudozero set; uncertainty; perturbation; stability.; pseudozero of of polynomial; root perturbation; computational stability; control theory
UR - http://eudml.org/doc/250033
ER -
References
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