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Asymptotics for Polynomial Zeros: Beware of Predictions from Plots

Asymptotics for Polynomial Zeros: Beware of Predictions from Plots We consider five plots of zeros corresponding to four eponymous planar polynomials (Szegő, Bergman, Faber and OPUC), for degrees up to 60, and state five conjectures suggested by these plots regarding their asymptotic distribution of zeros. By using recent results on zero distribution of polynomials we show that all these “natural” conjectures are false. Our main purpose is to provide the theoretical tools that explain, in each case, why these accurate, low degree plots are misleading in the asymptotic sense. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Computational Methods and Function Theory Springer Journals

Asymptotics for Polynomial Zeros: Beware of Predictions from Plots

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Heldermann  Verlag
Subject
Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
ISSN
1617-9447
eISSN
2195-3724
DOI
10.1007/BF03321695
Publisher site
See Article on Publisher Site

Abstract

We consider five plots of zeros corresponding to four eponymous planar polynomials (Szegő, Bergman, Faber and OPUC), for degrees up to 60, and state five conjectures suggested by these plots regarding their asymptotic distribution of zeros. By using recent results on zero distribution of polynomials we show that all these “natural” conjectures are false. Our main purpose is to provide the theoretical tools that explain, in each case, why these accurate, low degree plots are misleading in the asymptotic sense.

Journal

Computational Methods and Function TheorySpringer Journals

Published: Sep 20, 2007

References