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Dr. Pierre Lairez
- © Pierre Lairez
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
| 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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