Computing Hermitian determinantal representations of hyperbolic curves
Algebraic Geometry
2015-04-24 v1 Optimization and Control
Abstract
Every real hyperbolic form in three variables can be realized as the determinant of a linear net of Hermitian matrices containing a positive definite matrix. Such representations are an algebraic certificate for the hyperbolicity of the polynomial and their existence has been proved in several different ways. However, the resulting algorithms for computing determinantal representations are computationally intensive. In this note, we present an algorithm that reduces a large part of the problem to linear algebra and discuss its numerical implementation.
Cite
@article{arxiv.1504.06023,
title = {Computing Hermitian determinantal representations of hyperbolic curves},
author = {Daniel Plaumann and Rainer Sinn and David E. Speyer and Cynthia Vinzant},
journal= {arXiv preprint arXiv:1504.06023},
year = {2015}
}
Comments
8 pages, 2 figures