A Deterministic Algorithm to Compute Approximate Roots of Polynomial Systems in Polynomial Average Time

被引：0
|
作者：
Pierre Lairez
机构：
[1] Technische Universität Berlin,Institut für Mathematik
来源：
Foundations of Computational Mathematics | 2017年 / 17卷
关键词：
Polynomial system; Homotopy continuation; Complexity; Smale’s 17th problem; Derandomization; Primary 68Q25; Secondary 65H10; 65H20; 65Y20;
D O I：
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学科分类号：
摘要：
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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页码：1265 / 1292
页数：27
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