On the foundations of best approximation theory

DOI10.1016/0021-9045(80)90081-7zbMath0441.41013OpenAlexW1966234664MaRDI QIDQ1142944

Douglas S. Bridges

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1016/0021-9045(80)90081-7

zbMATH Keywords

Bishop's constructive analysisminimax polynomial approximations

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Approximation by polynomials (41A10)

Related Items (8)

Lipschitz Constants and Moduli of Continuity for the Chebyshev Projection ⋮ New effective moduli of uniqueness and uniform a priori estimates for constants of strong unicity by logical analysis of known proofs in best approximation theory ⋮ A constructive development of Chebyshev approximation theory ⋮ Computability of finite-dimensional linear subspaces and best approximation ⋮ A constructive analysis of the Remes algorithm ⋮ Effective moduli from ineffective uniqueness proofs. An unwinding of de La Vallée Poussin's proof for Chebycheff approximation ⋮ Computability of the Metric Projection Onto Finite-dimensional Linear Subspaces ⋮ Continuity and Lipschitz constants for projections

Cites Work

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• A constructive development of Chebyshev approximation theory
• A constructive proximinality property of finite-dimensional linear subspaces
• Principles of intuitionism. Lectures presented at the summer conference on intuitionism and proof theory (1968) at SUNY at Buffalo, NY
• Introduction to the constructive theory of functions
• On continuous Mappings between Locally Compact Metric Spaces
• A Criterion for Compactness in Metric Spaces?

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