Hyperinterpolation in the cube

DOI10.1016/j.camwa.2007.10.003zbMath1142.65312OpenAlexW2151881956MaRDI QIDQ945146

Stefano De Marchi, Marco Caliari, Marco Vianello

Publication date: 11 September 2008

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

Full work available at URL: https://doi.org/10.1016/j.camwa.2007.10.003

zbMATH Keywords

hyperinterpolationLebesgue constantnumerical cubature

Mathematics Subject Classification ID

Numerical interpolation (65D05) Numerical integration (65D30)

Related Items (11)

On the norm of the hyperinterpolation operator on the \(d\)-dimensional cube ⋮ Bypassing the quadrature exactness assumption of hyperinterpolation on the sphere ⋮ Is hyperinterpolation efficient in the approximation of singular and oscillatory functions? ⋮ Learning mixtures of polynomials of multidimensional probability densities from data using B-spline interpolation ⋮ Hyperinterpolation in the cube ⋮ On the norm of the hyperinterpolation operator on the unit ball ⋮ Nontensorial Clenshaw-Curtis cubature ⋮ New cubature formulae and hyperinterpolation in three variables ⋮ HyperCube ⋮ On the quadrature exactness in hyperinterpolation ⋮ Lasso Hyperinterpolation Over General Regions

Uses Software

• QSHEP3D
• Hyper2d
• Chebfun
• ACML

Cites Work

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• Improved cubature formulae of high degrees of exactness for the square
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• Multivariate polynomial approximation
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• Minimal cubature formulae of degree 2k-1 for two classical functionals
• Multivariate simultaneous approximation
• Polynomial interpolation and hyperinterpolation over general regions
• Polynomial interpolation in several variables
• Constructive polynomial approximation on the sphere
• On multivariate projection operators
• Hyperinterpolation on the square
• On the Lebesgue constant for the Xu interpolation formula
• Exact order of the Lebesgue constants for bivariate Lagrange interpolation at certain node-systems
• Multivariate interpolation of large sets of scattered data
• Construction of Algebraic Cubature Rules Using Polynomial Ideal Theory
• An Extension of MATLAB to Continuous Functions and Operators

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