Asymptotics for polynomial zeros: Beware of predictions from plots

DOI10.1007/BF03321695zbMath1163.30010OpenAlexW2073140015MaRDI QIDQ934555

Nikos S. Stylianopoulos, Edward B. Saff

Publication date: 29 July 2008

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf03321695

zbMATH Keywords

zeros of polynomialsSzegő polynomialsequilibrium measureFaber polynomialsBergman polynomialsOPUC

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Polynomials and rational functions of one complex variable (30C10) Kernel functions in one complex variable and applications (30C40)

Related Items (3)

Zeros of non-Baxter paraorthogonal polynomials on the unit circle ⋮ Bergman polynomials on an archipelago: estimates, zeros and shape reconstruction ⋮ Error analysis of the Bergman kernel method with singular basis functions

Uses Software

• Schwarz-Christoffel
• SC Toolbox
• CONFPACK

Cites Work

• Asymptotic behaviour of zeros of Bieberbach polynomials
• Zero distributions for polynomials orthogonal with weights over certain planar regions
• Stability and convergence properties of Bergman kernel methods for numerical conformal mapping
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• Perturbation of orthogonal polynomials on an arc of the unit circle. II
• Erdős-Turán type theorems on quasiconformal curves and arcs
• The zeros of Faber polynomials for an \(m\)-cusped hypocycloid
• Zero distribution of Bergman orthogonal polynomials for certain planar domains
• \(L^2\)-approximations of power and logarithmic functions with applications to numerical conformal mapping
• Zeros of polynomials orthogonal over regular \(N\)-gons.
• Approximation of conformal mapping via the Szegő kernel method
• On Faber polynomials and Faber expansions
• On the distribution of zeros of polynomials orthogonal on the unit circle
• On the decrease of Faber polynomials in domains with piecewise analytic boundary
• The Bergman Kernel Method for the Numerical Conformal Mapping of Simply Connected Domains
• Algorithm 756: a MATLAB toolbox for Schwarz-Christoffel mapping
• Asymptotic distribution of the zeros of Faber polynomials
• Konstruktive Methoden der konformen Abbildung
• Fine structure of the zeros of orthogonal polynomials III: Periodic recursion coefficients
• Polynomials of Interpolation and Approximation to Meromorphic Functions
• Convergence of Bieberbach polynomials in domains with interior cusps
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