Enhancing the approximation order of local Shepard operators by Hermite polynomials

DOI10.1016/j.camwa.2012.10.004zbMath1268.41019OpenAlexW2145630947MaRDI QIDQ356379

Francesco Aldo Costabile, F. Di Tommaso, Francesco Dell'Accio

Publication date: 25 July 2013

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2012.10.004

zbMATH Keywords

error analysisHermite interpolationShepard operatoralgebraic precision

Mathematics Subject Classification ID

Linear programming (90C05) Numerical interpolation (65D05) Approximation by operators (in particular, by integral operators) (41A35)

Related Items (12)

A meshless interpolation algorithm using a cell-based searching procedure ⋮ Max-product Shepard operators based on multivariable Taylor polynomials ⋮ Hermite-Birkhoff interpolation on scattered data on the sphere and other manifolds ⋮ Reconstruction of a function from Hermite-Birkhoff data ⋮ Fast computation of triangular Shepard interpolants ⋮ Optimal order Jackson type inequality for scaled Shepard approximation ⋮ On the linearization methods for univariate Birkhoff rational interpolation ⋮ Bivariate Shepard-Bernoulli operators ⋮ A mixed Lagrange-Bernoulli tensor product expansion on the rectangle with applications ⋮ Unnamed Item ⋮ Complete Hermite-Birkhoff interpolation on scattered data by combined Shepard operators ⋮ Modified Shepard's method by six-points local interpolant

Uses Software

• QSHEP3D
• Algorithm 792

Cites Work

• Unnamed Item
• Complementary Lidstone interpolation on scattered data sets
• An asymptotic expansion for the error in a linear map that reproduces polynomials of a certain order
• Error estimates for modified local Shepard's interpolation formula
• Multivariate vertex splines and finite elements
• Increasing the polynomial reproduction of a quasi-interpolation operator
• Enhancement of the algebraic precision of a linear operator and consequences under positivity
• A triangle-based \(C^ 1\) interpolation method
• Multi-node higher order expansions of a function.
• On the bivariate Shepard-Lidstone operators
• Multivariate approximation by a combination of modified Taylor polynomials
• General Lagrange and Hermite interpolation in \(R^n\) with applications to finite element methods
• Rate of Convergence of Shepard's Global Interpolation Formula
• Multivariate interpolation of large sets of scattered data
• Algorithm 792
• Modified Taylor reproducing formulas and \emph{h-p} clouds
• Scattered Data Approximation

This page was built for publication: Enhancing the approximation order of local Shepard operators by Hermite polynomials