Computing Hermitian determinantal representations of hyperbolic curves
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.
 Publication:

arXiv eprints
 Pub Date:
 April 2015
 arXiv:
 arXiv:1504.06023
 Bibcode:
 2015arXiv150406023P
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Optimization and Control
 EPrint:
 8 pages, 2 figures