Behavior of Polynomials of Best Uniform Approximation

DOI10.2307/2001362zbMath0683.41034OpenAlexW4247319105MaRDI QIDQ4732862

Vilmos Totik, Edward B. Saff

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2001362

zbMATH Keywords

best uniform approximation

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Approximation by polynomials (41A10)

Related Items (13)

Polynomial approximation on the boundary and strictly inside ⋮ Polynomial approximation and maximal convergence on Faber sets ⋮ Massiveness of the sets of extremal functions in some problems in approximation theory ⋮ Degree of approximation of analytic functions by ``near-best polynomial approximants ⋮ Behavior of polynomials of best \(H^ p\) approximation ⋮ Limitations of the Carathéodory-Fejér method for polynomial approximation ⋮ Discrete approximating operators on function algebras ⋮ Approximation of analytic functions by polynomials ``close to polynomials of best approximation ⋮ ``Near-best polynomial approximation of harmonic functions on compact sets in \(\mathbb{C}\) ⋮ On the distribution of alternation points in uniform polynomial approximation of entire functions ⋮ Extended best \(L^p\)-approximation is near-best approximation in \(L^q, p - 1 \leq q < p\) ⋮ Polynomial approximation of piecewise analytic functions on quasi-smooth arcs ⋮ Simultaneous approximation and interpolation of functions on continua in the complex plane.

Cites Work

• The distribution of extreme points in best complex polynomial approximation
• Isomorphisms of the disc algebra and inverse Faber sets
• Near-circularity of the error curve in complex Chebyshev approximation
• Topics in approximation theory
• On the order of polynomial approximation for closed Jordan domains
• Limitations of the Carathéodory-Fejér method for polynomial approximation
• The Carathéodory–Fejér Method for Real Rational Approximation
• The Density of Extreme Points in Complex Polynomial Approximation
• Jentzsch-Szegö Type Theorems for the Zeros of Best Approximants
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