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arXiv · 1212.3506

Determinantal representations of hyperbolic curves via polynomial homotopy continuation

Anton Leykin·Daniel Plaumann
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Abstract

A smooth curve in the real projective plane is hyperbolic if its ovals are maximally nested. By the Helton-Vinnikov Theorem, any such curve admits a definite symmetric determinantal representation. We use polynomial homotopy continuation to compute such representations numerically. Our method works by lifting paths from the space of hyperbolic polynomials to a branched cover in the space of pairs of symmetric matrices.

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Anton Leykin, Daniel Plaumann. 2016-07-04. Determinantal representations of hyperbolic curves via polynomial homotopy continuation. https://arxiv.org/abs/1212.3506

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