A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time
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.
Fichier principal
archive.deterministic_algorithm.pdf (714.54 Ko)
Télécharger le fichier
calculator.pdf (2.35 Ko)
Télécharger le fichier
Origin : Files produced by the author(s)
Origin : Files produced by the author(s)