On the Degree of Convergence of Piecewise Polynomial Approximation on Optimal Meshes

DOI10.2307/1997935zbMath0366.41009OpenAlexW4241739814MaRDI QIDQ4142176

Hermann G. Burchard

Publication date: 1977

Full work available at URL: https://doi.org/10.2307/1997935

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Singular functions, Cantor functions, functions with other special properties (26A30) Rate of convergence, degree of approximation (41A25) Spline approximation (41A15)

Related Items (max. 100)

A Bernstein-type inequality associated with wavelet decomposition ⋮ An adaptive algorithm for multivariate approximation giving optimal convergence rates ⋮ On the degree of nonlinear spline approximation in Besov-Sobolev spaces ⋮ Product Integration-Collocation Methods for Noncompact Integral Operator Equations ⋮ Analysis of an algorithm for generating locally optimal meshes for 𝐿₂ approximation by discontinuous piecewise polynomials

Cites Work

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• Piecewise polynomial approximation on optimal meshes
• On Polya frequency functions. IV: The fundamental spline functions and their limits
• On the fundamental approximation theorems of D. Jackson, S.N. Bernstein and theorems of M. Zamansky and S.B. Stechkin
• On uniform approximation by splines
• Splines (with optimal knots) are better
• Nonlinear segmented function approximation and analysis of line patterns

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