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arXiv · 1507.05485

A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time

Pierre Lairez
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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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Pierre Lairez. 2016-05-19. A deterministic algorithm to compute approximate roots of polynomial systems in polynomial average time. https://doi.org/10.1007/s10208-016-9319-7

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