Name
Abstract | ||
|---|---|---|
Motivated by Wilmshurst's conjecture, we investigate the zeros of harmonic polynomials. We utilize a certified counting approach, which is a combination of two methods from numerical algebraic geometry: numerical polynomial homotopy continuation to compute a numerical approximation of each zero and Smale's alpha theory to certify the results. We provide new examples of harmonic polynomials having the most extreme number of zeros known so far; we also study the mean and variance of the number of zeros of random harmonic polynomials. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1080/10586458.2014.966180 | EXPERIMENTAL MATHEMATICS |
Keywords | Field | DocType |
harmonic polynomials,Wilmshurst's conjecture,homotopy continuation,alpha-certification,root-finding | Wilson polynomials,Topology,Classical orthogonal polynomials,Orthogonal polynomials,Mathematical analysis,Macdonald polynomials,Discrete orthogonal polynomials,Gegenbauer polynomials,Hahn polynomials,Mathematics,Difference polynomials | Journal |
Volume | Issue | ISSN |
24.0 | 2.0 | 1058-6458 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jonathan D. Hauenstein | 1 | 269 | 37.65 |
| antonio lerario | 2 | 1 | 1.64 |
| Erik Lundberg | 3 | 1 | 1.98 |
| Dhagash Mehta | 4 | 15 | 8.26 |