Work

Computing Hermitian determinantal representations of hyperbolic curves

Year: 2015

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1504.06023

Authors: Plaumann, Daniel, Sinn, Rainer, Speyer, David E., Vinzant, Cynthia

Institutions: University of Konstanz, Georgia Institute of Technology, University of Michigan, North Carolina State University

Language: English

Topic: Polynomial and algebraic computation

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2949538386

Cites: 1

Cited by:

Related to: 20