TU Berlin

Fachgebiet Algorithmische AlgebraDr. Pierre Lairez

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Dr. Pierre Lairez

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

Publikationen in der Arbeitsgruppe

A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time
Citation key L-A-Deterministic-Algorithm-To-Compute-Approximate-Roots-Of-Polynomial-Systems-In-Polynomial-Average-Time
Author Pierre Lairez
Year 2015
Month 10
Note To appear in Foundations of computational mathematics (2016), 23 pages.
Abstract We describe a deterministic algorithm that computes an approximate root of n complex polynomial equations in n unknowns in average polynomial time with respect to the size of the input, in the Blum-Shub-Smale model with square root. It rests upon a derandomization of an algorithm of Beltrán and Pardo and gives a deterministic affirmative answer to Smale's 17th problem. The main idea is to make use of the randomness contained in the input itself.
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