Bounds for the Condition Number of Polynomials Systems with Integer Coefficients - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Communication Dans Un Congrès Année : 2015

Bounds for the Condition Number of Polynomials Systems with Integer Coefficients

Aaron Herman
  • Fonction : Auteur
  • PersonId : 974181
Elias Tsigaridas

Résumé

Polynomial systems of equations are a central object of study in computer algebra. Among the many existing algorithms for solving polynomial systems, perhaps the most successful numerical ones are the homotopy algorithms. The number of operations that these algorithms perform depends on the condition number of the roots of the polynomial system. Roughly speaking the condition number expresses the sensitivity of the roots with respect to small perturbation of the input coefficients. A natural question to ask is how can we bound, in the worst case, the condition number when the input polynomials have integer coefficients? We address this problem and we provide effective bounds that depend on the number of variables, the degree and the maximum coefficient bitsize of the input polynomials. Such bounds allows to estimate the bit complexity of the algorithms that depend on the separation bound, like the homotopy algorithms, for solving polynomial systems.
Fichier principal
Vignette du fichier
dmm-cond.pdf (319.19 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01248389 , version 1 (25-12-2015)

Identifiants

Citer

Aaron Herman, Elias Tsigaridas. Bounds for the Condition Number of Polynomials Systems with Integer Coefficients. CASC, 2015, Aachen, Germany. pp.210--219, ⟨10.1007/978-3-319-24021-3_16⟩. ⟨hal-01248389⟩
149 Consultations
202 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More