Behavior of zeros of polynomials of near best approximation

DOI10.1016/0021-9045(86)90069-9zbMath0605.41026OpenAlexW2012228256MaRDI QIDQ1084274

Hans-Peter Blatt, Edward B. Saff

Publication date: 1986

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-9045(86)90069-9

zbMATH Keywords

near best approximationzeros of the polynomials of best uniform approximation

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Approximation in the complex plane (30E10) Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15)

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Local limiting behavior of the zeros of approximating polynomials, Poles and zeros of best rational approximants of \(| x|\), Convergence of Padé approximants of partial theta functions and the Rogers-Szegö polynomials, On zeros of polynomials of best approximation to holomorphic and \(C^{\infty}\) functions, Growth Behavior and Zero Distribution of Maximally Convergent Rational Approximants, Some applications of the Robin function to multivariable approximation theory, Exact maximal convergence in capacity and zero distribution of rational approximants, On the measure of the absolutely continuous spectrum for Jacobi matrices, On the distribution of zeros and poles of rational approximants on intervals, On the zeros of polynomials of best approximation, Growth behavior and zero distribution of rational approximants, Some remarks on Bernstein's theorems, The Jentzsch-Szegő theorem and balayage measures, The impact of poles on the convergence of best rational approximants, On a generalization of Jentzsch's theorem, Convergence of Julia polynomials, Polynomial approximation of piecewise analytic functions on quasi-smooth arcs

Cites Work

• On the asymptotic behavior of polynomials with extremal properties, and of their zeros
• The analogue for maximally convergent polynomials of Jentzsch's theorem
• Overconvergence, degree of convergence and zeros of sequences of analytic functions
• The Relationship Between the Zeros of Best Approximations and Differentiability
• On the distribution of points of maximum deviation in the approximation of continuous functions by polynomials
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