Simple determinantal representations of up to quintic bivariate polynomials

Abstract

For bivariate polynomials of degree $n\le 5$ we give fast numerical constructions of determinantal representations with $n\times n$ matrices. Unlike some other available constructions, our approach returns matrices of the smallest possible size $n\times n$ for all polynomials of degree $n$ and does not require any symbolic computation. We can apply these linearizations to numerically compute the roots of a system of two bivariate polynomials by using numerical methods for two-parameter eigenvalue problems.

24 pages, 5 figures

References in corpus (2)

• Roots of bivariate polynomial systems via determinantal representations
• Minimal determinantal representations of bivariate polynomials

Cited by in corpus (2)

• Minimal determinantal representations of bivariate polynomials
• Hessian matrices, automorphisms of $p$-groups, and torsion points of elliptic curves