Name
Title | ||
|---|---|---|
Determinantal representations of hyperbolic curves via polynomial homotopy continuation |
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 [d/2] 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. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1090/mcom/3194 | MATHEMATICS OF COMPUTATION |
Field | DocType | Volume |
Real projective plane,Topology,Polynomial,Hyperbolic tree,Mathematical analysis,Symmetric matrix,Hyperbolic manifold,Homotopy continuation,Smoothness,Mathematics | Journal | 86 |
Issue | ISSN | Citations |
308 | 0025-5718 | 1 |
PageRank | References | Authors |
0.36 | 2 | 2 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Anton Leykin | 1 | 173 | 18.99 |
| Daniel Plaumann | 2 | 38 | 8.86 |