[Formules générales pour l'analyse régularisée des nombres de conditionnement]
Nous donnons des estimations du volume de l'intersection des voisinages tubulaires autour d'une sous-variété Σ de l'espace projectif réel avec un disque de rayon σ. Les bornes s'expriment en fonction de σ, de la dimension de l'espace ambiant, et du degré des équations définissant Σ. Nous utilisons ces bornes pour obtenir des estimations au sens de l'analyse régularisé pour des nombres de conditionnement coniques.
We provide estimates on the volume of tubular neighborhoods around a subvariety Σ of real projective space, intersected with a disk of radius σ. The bounds are in terms of σ, the dimension of the ambient space, and the degree of equations defining Σ. We use these bounds to obtain smoothed analysis estimates for some conic condition numbers.
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@article{CRMATH_2006__343_2_145_0,
author = {B\"urgisser, Peter and Cucker, Felipe and Lotz, Martin},
title = {General formulas for the smoothed analysis of condition numbers},
journal = {Comptes Rendus. Math\'ematique},
pages = {145--150},
publisher = {Elsevier},
volume = {343},
number = {2},
year = {2006},
doi = {10.1016/j.crma.2006.05.014},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.05.014/}
}
TY - JOUR AU - Bürgisser, Peter AU - Cucker, Felipe AU - Lotz, Martin TI - General formulas for the smoothed analysis of condition numbers JO - Comptes Rendus. Mathématique PY - 2006 SP - 145 EP - 150 VL - 343 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.05.014/ DO - 10.1016/j.crma.2006.05.014 LA - en ID - CRMATH_2006__343_2_145_0 ER -
%0 Journal Article %A Bürgisser, Peter %A Cucker, Felipe %A Lotz, Martin %T General formulas for the smoothed analysis of condition numbers %J Comptes Rendus. Mathématique %D 2006 %P 145-150 %V 343 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.05.014/ %R 10.1016/j.crma.2006.05.014 %G en %F CRMATH_2006__343_2_145_0
Bürgisser, Peter; Cucker, Felipe; Lotz, Martin. General formulas for the smoothed analysis of condition numbers. Comptes Rendus. Mathématique, Tome 343 (2006) no. 2, pp. 145-150. doi : 10.1016/j.crma.2006.05.014. http://www.numdam.org/articles/10.1016/j.crma.2006.05.014/
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