TU Berlin

Fachgebiet Algorithmische AlgebraDr. Pierre Lairez

Inhalt des Dokuments

zur Navigation

Ehemalige Mitarbeiter

Dr. Pierre Lairez

Lupe

Anschrift
INRIA Saclay Île-de-France, Bât. Alan Turing
1 rue Honoré d'Estienne d'Orves
Campus de l'École polytechnique
91120 Palaiseau
France
 
Persönliche Homepage
pierre.lairez.fr

Publikationen in der Arbeitsgruppe

Rigid continuation paths II. Structured polynomial systems
Zitatschlüssel BCL-RigidContinuationPathsII-StructuredPolynomialSystems
Autor Peter Bürgisser and Felipe Cucker and Pierre Lairez
Jahr 2020
Zusammenfassung We design a probabilistic algorithm that, given ϵ>0 and a polynomial system F given by black-box evaluation functions, outputs an approximate zero of F, in the sense of Smale, with probability at least 1−ϵ. When applying this algorithm to u⋅F, where u is uniformly random in the product of unitary groups, the algorithm performs poly(n,δ)⋅L(F)⋅(Γ(F)logΓ(F)+log log ϵ^(−1)) operations on average. Here n is the number of variables, δ the maximum degree, L(F) denotes the evaluation cost of F, and Γ(F) reflects an aspect of the numerical condition of F. Moreover, we prove that for inputs given by random Gaussian algebraic branching programs of size poly(n,δ), the algorithm runs on average in time polynomial in n and δ. Our result may be interpreted as an affirmative answer to a refined version of Smale's 17th question, concerned with systems of \emphstructured polynomial equations.
Link zur Publikation Download Bibtex Eintrag

Navigation

Direktzugang

Schnellnavigation zur Seite über Nummerneingabe