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.

Experiments on the zeroes of harmonic polynomials using certified counting

Lerario, Antonio;
2015

Abstract

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.
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https://arxiv.org/abs/1406.5523
Hauenstein, J. D.; Lerario, Antonio; Lundberg, E.; Mehta, D.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/32524
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