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Determinantal representations of hyperbolic curves via polynomial homotopy continuation

Determinantal representations of hyperbolic curves via polynomial homotopy continuation

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LEYKIN, Anton, Daniel PLAUMANN, 2017. Determinantal representations of hyperbolic curves via polynomial homotopy continuation. In: Mathematics of Computation. 86(308), pp. 2877-2888. ISSN 0025-5718. eISSN 1088-6842

@article{Leykin2017Deter-39627, title={Determinantal representations of hyperbolic curves via polynomial homotopy continuation}, year={2017}, doi={10.1090/mcom/3194}, number={308}, volume={86}, issn={0025-5718}, journal={Mathematics of Computation}, pages={2877--2888}, author={Leykin, Anton and Plaumann, Daniel} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/39627"> <dc:contributor>Leykin, Anton</dc:contributor> <dc:contributor>Plaumann, Daniel</dc:contributor> <dc:creator>Plaumann, Daniel</dc:creator> <dc:language>eng</dc:language> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/39627"/> <dc:creator>Leykin, Anton</dc:creator> <dcterms:abstract xml:lang="eng">A smooth curve of degree $ d$ in the real projective plane is hyperbolic if its ovals are maximally nested, i.e., its real points contain $ \lfloor \frac d2\rfloor $ nested ovals. 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.</dcterms:abstract> <dcterms:title>Determinantal representations of hyperbolic curves via polynomial homotopy continuation</dcterms:title> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-07-19T09:31:06Z</dc:date> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2017-07-19T09:31:06Z</dcterms:available> <dcterms:issued>2017</dcterms:issued> </rdf:Description> </rdf:RDF>

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