Shepard--Bernoulli operators

DOI10.1090/S0025-5718-06-01894-1zbMath1106.41019OpenAlexW2077278596MaRDI QIDQ3420433

Rosanna Caira, Francesco Dell'Accio

Publication date: 2 February 2007

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-06-01894-1

zbMATH Keywords

interpolationrate of convergence

Mathematics Subject Classification ID

Numerical interpolation (65D05) Approximation by operators (in particular, by integral operators) (41A35)

Related Items

An iterative modification of Shepard-Bernoulli operator ⋮ Complementary Lidstone interpolation on scattered data sets ⋮ Max-product Shepard operators based on multivariable Taylor polynomials ⋮ Increasing the approximation order of the triangular Shepard method ⋮ Reconstruction of a function from Hermite-Birkhoff data ⋮ A kind of bivariate Bernoulli-type multiquadric quasi-interpolation operator with higher approximation order ⋮ On the bivariate Shepard-Lidstone operators ⋮ The bivariate Shepard operator of Bernoulli type ⋮ Bivariate Shepard-Bernoulli operators ⋮ Abel-Goncharov type multiquadric quasi-interpolation operators with higher approximation order ⋮ Complex Shepard operators and their summability ⋮ Bivariate quasi-interpolation operator of Bernoulli type ⋮ A kind of improved univariate multiquadric quasi-interpolation operators ⋮ Complete Hermite-Birkhoff interpolation on scattered data by combined Shepard operators ⋮ New bivariate polynomial expansion with boundary data on the simplex ⋮ On the hexagonal Shepard method ⋮ Modified Shepard's method by six-points local interpolant

Uses Software

• QSHEP2D
• QSHEP3D

Cites Work

• Error estimates for modified local Shepard's interpolation formula
• A triangle-based \(C^ 1\) interpolation method
• Shepard operators of Birkhoff-type
• Algorithm 661
• Algorithm 660: QSHEP2D: Quadratic Shepard Method for Bivariate Interpolation of Scattered Data
• Rate of Convergence of Shepard's Global Interpolation Formula
• Multivariate interpolation of large sets of scattered data
• Comparing Numerical Methods for Ordinary Differential Equations
• Expansion over a rectangle of real functions in Bernoulli polynomials and applications
• Expansions over a simplex of real functions by means of Bernoulli polynomials
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