Motivated by Wilmshursts 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 Smales 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. © 2015 Taylor and Francis Group, LLC.
Titolo: | Experiments on the zeroes of harmonic polynomials using certified counting |
Autori: | Hauenstein, J.D.; Lerario, A.; Lundberg, E.; Mehta, D. |
Rivista: | |
Data di pubblicazione: | 2015 |
Volume: | 24 |
Fascicolo: | 2 |
Pagina iniziale: | 133 |
Pagina finale: | 141 |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1080/10586458.2014.966180 |
URL: | https://arxiv.org/abs/1406.5523 |
Appare nelle tipologie: | 1.1 Journal article |
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