Name
Abstract | ||
|---|---|---|
Given a homotopy connecting two polynomial systems, we provide a rigorous algorithm for tracking a regular homotopy path connecting an approximate zero of the start system to an approximate zero of the target system. Our method uses recent results on the complexity of homotopy continuation rooted in the alpha theory of Smale. Experimental results obtained with an implementation in the numerical algebraic geometry package Macaulay2 demonstrate the practicality of the algorithm. In particular, we confirm the theoretical results for random linear homotopies and illustrate the plausibility of a conjecture by Shub and Smale on a good initial pair. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1080/10586458.2011.606184 | EXPERIMENTAL MATHEMATICS |
Keywords | Field | DocType |
Computational aspects of algebraic geometry,systems of equations,continual methods,homotopy methods,approximate zero,certified algorithms,complexity | Topology,System of linear equations,Polynomial,Algebra,Mathematical analysis,n-connected,Cofibration,Homotopy,Homotopy analysis method,Regular homotopy,Homotopy lifting property,Mathematics | Journal |
Volume | Issue | ISSN |
21.0 | 1.0 | 1058-6458 |
Citations | PageRank | References |
10 | 0.68 | 8 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Carlos Beltrán | 1 | 102 | 10.04 |
| Anton Leykin | 2 | 173 | 18.99 |