Fast Computation of Zeros of Polynomial Systems with Bounded Degree under Finite-precision
Numerical Analysis
2012-05-07 v1
Abstract
A solution for Smale's 17th problem, for the case of systems with bounded degree was recently given. This solution, an algorithm computing approximate zeros of complex polynomial systems in average polynomial time, assumed infinite precision. In this paper we describe a finite-precision version of this algorithm. Our main result shows that this version works within the same time bounds and requires a precision which, on the average, amounts to a polynomial amount of bits in the mantissa of the intervening floating-point numbers.
Keywords
Cite
@article{arxiv.1205.0869,
title = {Fast Computation of Zeros of Polynomial Systems with Bounded Degree under Finite-precision},
author = {Irenee Briquel and Felipe Cucker and Javier Pena and Vera Roshchina},
journal= {arXiv preprint arXiv:1205.0869},
year = {2012}
}