Determinantal representations of hyperbolic curves via polynomial homotopy continuation
| dc.contributor.author | Leykin, Anton | |
| dc.contributor.author | Plaumann, Daniel | |
| dc.date.accessioned | 2017-07-19T09:31:06Z | |
| dc.date.available | 2017-07-19T09:31:06Z | |
| dc.date.issued | 2017 | eng |
| dc.description.abstract | 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. | eng |
| dc.description.version | published | de |
| dc.identifier.doi | 10.1090/mcom/3194 | eng |
| dc.identifier.uri | https://kops.uni-konstanz.de/handle/123456789/39627 | |
| dc.language.iso | eng | eng |
| dc.subject.ddc | 510 | eng |
| dc.title | Determinantal representations of hyperbolic curves via polynomial homotopy continuation | eng |
| dc.type | JOURNAL_ARTICLE | de |
| dspace.entity.type | Publication | |
| kops.citation.bibtex | @article{Leykin2017Deter-39627,
year={2017},
doi={10.1090/mcom/3194},
title={Determinantal representations of hyperbolic curves via polynomial homotopy continuation},
number={308},
volume={86},
issn={0025-5718},
journal={Mathematics of Computation},
pages={2877--2888},
author={Leykin, Anton and Plaumann, Daniel}
} | |
| kops.citation.iso690 | LEYKIN, Anton, Daniel PLAUMANN, 2017. Determinantal representations of hyperbolic curves via polynomial homotopy continuation. In: Mathematics of Computation. 2017, 86(308), pp. 2877-2888. ISSN 0025-5718. eISSN 1088-6842. Available under: doi: 10.1090/mcom/3194 | deu |
| kops.citation.iso690 | LEYKIN, Anton, Daniel PLAUMANN, 2017. Determinantal representations of hyperbolic curves via polynomial homotopy continuation. In: Mathematics of Computation. 2017, 86(308), pp. 2877-2888. ISSN 0025-5718. eISSN 1088-6842. Available under: doi: 10.1090/mcom/3194 | eng |
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<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>
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| kops.sourcefield | Mathematics of Computation. 2017, <b>86</b>(308), pp. 2877-2888. ISSN 0025-5718. eISSN 1088-6842. Available under: doi: 10.1090/mcom/3194 | deu |
| kops.sourcefield.plain | Mathematics of Computation. 2017, 86(308), pp. 2877-2888. ISSN 0025-5718. eISSN 1088-6842. Available under: doi: 10.1090/mcom/3194 | deu |
| kops.sourcefield.plain | Mathematics of Computation. 2017, 86(308), pp. 2877-2888. ISSN 0025-5718. eISSN 1088-6842. Available under: doi: 10.1090/mcom/3194 | eng |
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