Testing hyperbolicity of real polynomials

2018/10/08 by Dey, Papri, Plaumann, Daniel
#Algebraic Geometry (math.AG) #FOS: Mathematics #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1810.04055

Abstract

Hyperbolic polynomials are real multivariate polynomials with only real roots along a fixed pencil of lines. Testing whether a given polynomial is hyperbolic is a difficult task in general. We examine different ways of translating hyperbolicity into nonnegativity conditions, which can then be tested via sum-of-squares relaxations.

Related

• Real Stability Testing
• Certifying polynomial nonnegativity via hyperbolic optimization
• Hyperbolicity and stable polynomials in combinatorics and probability
• Hyperbolic polynomials and the Marcus-Spielman-Srivastava theorem
• Linear slices of hyperbolic polynomials and positivity of symmetric polynomial functions