A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time
Numerical Analysis
2023-06-12 v3 Computational Complexity
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 Beltr\'an 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.
Cite
@article{arxiv.1507.05485,
title = {A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time},
author = {Pierre Lairez},
journal= {arXiv preprint arXiv:1507.05485},
year = {2023}
}