Increasing the polynomial reproduction of a quasi-interpolation operator

DOI10.1016/j.jat.2008.08.011zbMath1181.41009OpenAlexW2033729283MaRDI QIDQ1040858

Shayne F. D. Waldron

Publication date: 26 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.jat.2008.08.011

zbMATH Keywords

finite element methodBernstein polynomialquasi-interpolationChau-Vandermonde convolutionmultipoint Taylor formula

Mathematics Subject Classification ID

Linear operator methods in interpolation, moment and extension problems (47A57) Interpolation in approximation theory (41A05) Approximation by polynomials (41A10)

Related Items (7)

Enhancing the approximation order of local Shepard operators by Hermite polynomials ⋮ A kind of multiquadric quasi-interpolation operator satisfying any degree polynomial reproduction property to scattered data ⋮ Univariate Lidstone-type multiquadric quasi-interpolants ⋮ A family of multivariate multiquadric quasi-interpolation operators with higher degree polynomial reproduction ⋮ High accuracy B-spline quasi-interpolants and applications in numerical analysis ⋮ Raising the approximation order of multivariate quasi-interpolants ⋮ Unnamed Item

Cites Work

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• An asymptotic expansion for the error in a linear map that reproduces polynomials of a certain order
• A formula for Kergin interpolation in \(R^ k\).
• Multipoint Taylor formulae
• Integral error formulae for the scale of mean value interpolations which includes Kergin and Hakopian interpolation
• Multi-node higher order expansions of a function.
• Multivariate approximation by a combination of modified Taylor polynomials
• The degree of approximation by polynomials with positive coefficients
• Refinements of the peano kernel theorem

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