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Explicit determinantal representations of up to quintic bivariate polynomials
Buckley, Anita ; Plestenjak, Bor
For bivariate polynomials of degree ▫$n \le 5$▫ we give fast numerical constructions of determinantal representations with ▫$n \times n$▫ matrices. Unlike some other existing constructions, our ...approach returns matrices of the smallest possible size ▫$n \times n$▫ for all (not just generic) polynomials of degreen 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 the two-parameter eigenvalue problems.
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