Determinantal representations of hyperbolic curves via polynomial homotopy continuation
Algebraic Geometry
2016-07-05 v3 Optimization and Control
Abstract
A smooth curve in the real projective plane is hyperbolic if its ovals are maximally nested. By the Helton-Vinnikov Theorem, any such curve admits a definite symmetric determinantal representation. We use polynomial homotopy continuation to compute such representations numerically. Our method works by lifting paths from the space of hyperbolic polynomials to a branched cover in the space of pairs of symmetric matrices.
Keywords
Cite
@article{arxiv.1212.3506,
title = {Determinantal representations of hyperbolic curves via polynomial homotopy continuation},
author = {Anton Leykin and Daniel Plaumann},
journal= {arXiv preprint arXiv:1212.3506},
year = {2016}
}
Comments
minor corrections and additions, 13 pages