Geometry and topology of continuous best and near best approximations

DOI10.1006/jath.2000.3467zbMath0969.41020OpenAlexW2010261079MaRDI QIDQ1583970

Andrew Vogt, Paul C. Kainen, Vera Kurková

Publication date: 5 February 2001

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

Full work available at URL: http://www.nusl.cz/ntk/nusl-33841

zbMATH Keywords

continuous selectionsmodulus of convexityChebyshev setsnear best approximationChebyshev radius- best approximationstrictly and uniformly convex norms

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Geometry and structure of normed linear spaces (46B20) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (8)

On the nonuniqueness and instability of solutions of tracking-type optimal control problems ⋮ A Sobolev-type upper bound for rates of approximation by linear combinations of Heaviside plane waves ⋮ Probabilistic lower bounds for approximation by shallow perceptron networks ⋮ Best approximation by linear combinations of characteristic functions of half-spaces. ⋮ Minimization of Error Functionals over Perceptron Networks ⋮ Integral combinations of Heavisides ⋮ Some comparisons of complexity in dictionary-based and linear computational models ⋮ Approximative compactness of linear combinations of characteristic functions

Cites Work

• Continuities of metric projection and geometric consequences
• Optimal nonlinear approximation
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