Year: 2022
Type: preprint
Abstract: We study the class of polynomials whose Hessians evaluated at any point of a closed convex cone have Lorentzian signature. This class is a generalization to the remarkable class of Lorentzian polynomials. We prove that hyperbolic polynomials and conic stable polynomials belong to this class, and the set of polynomials with Lorentzian signature is closed. Finally, we develop a method for computing permanents of nonsingular matrices which belong to a class that includes nonsingular $k$-locally singular matrices via hyperbolic programming.
Source: arXiv (Cornell University)
Author: Dey, Papri
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4302009015