Experiments on the Zeros of Harmonic Polynomials Using Certified Counting

DOI10.1080/10586458.2014.966180zbMath1365.30002arXiv1406.5523OpenAlexW2056969837WikidataQ115997087 ScholiaQ115997087MaRDI QIDQ5264646

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Publication date: 27 July 2015

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.5523

zbMATH Keywords

homotopy continuationharmonic polynomialsWilmshurst's conjectureroot-findingalpha-certification

Mathematics Subject Classification ID

Computational aspects of algebraic curves (14Q05) Algorithms with automatic result verification (65G20) Polynomials and rational functions of one complex variable (30C10) Numerical computation of roots of polynomial equations (65H04)

Related Items (9)

Multiplane gravitational lenses with an abundance of images ⋮ The valence of harmonic polynomials viewed through the probabilistic lens ⋮ On the number of roots for harmonic trinomials ⋮ On the numbers of images of two stochastic gravitational lensing models ⋮ A Survey on the Maximal Number of Solutions of Equations Related to Gravitational Lensing ⋮ A new lower bound for the maximal valence of harmonic polynomials ⋮ Zeros of harmonic polynomials, critical lemniscates, and caustics ⋮ Location of the zeros of harmonic trinomials ⋮ On the zeros of random harmonic polynomials: the truncated model

Uses Software

• Bertini

Cites Work

• Unnamed Item
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• Algorithm 921
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