Year: 2011
Type: preprint
Abstract: Given a polynomial system f, a fundamental question is to determine if f has real roots. Many algorithms involving the use of infinitesimal deformations have been proposed to answer this question. In this article, we transform an approach of Rouillier, Roy, and Safey El Din, which is based on a classical optimization approach of Seidenberg, to develop a homotopy based approach for computing at least one point on each connected component of a real algebraic set. Examples are presented demonstrating the effectiveness of this parallelizable homotopy based approach.
Source: arXiv (Cornell University)
Author: Hauenstein, Jonathan D.
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950314807