Chebyshev lattices, a unifying framework for cubature with Chebyshev weight function

DOI10.1007/s10543-010-0300-6zbMath1222.65025OpenAlexW2077609376WikidataQ57778812 ScholiaQ57778812MaRDI QIDQ634123

Ronald Cools, Koen Poppe

Publication date: 2 August 2011

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-010-0300-6

zbMATH Keywords

cubaturehyperinterpolationPadua pointsChebyshev latticesGodzina's blending formulaeMorrow-Patterson pointsmultivariate Clenshaw-Curtis

Mathematics Subject Classification ID

Numerical quadrature and cubature formulas (65D32)

Related Items

Bivariate Lagrange interpolation at the node points of non-degenerate Lissajous curves, Multivariate polynomial interpolation on Lissajous-Chebyshev nodes, In Search for Good Chebyshev Lattices, Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk, Cubature, Approximation, and Isotropy in the Hypercube, Least Squares Approximation of Polynomial Chaos Expansions With Optimized Grid Points, Hyperinterpolation for Spectral Wave Propagation Models in Three Dimensions, Bivariate Lagrange interpolation at the node points of Lissajous curves -- the degenerate case, Schemes for cubature over the unit disk found via numerical optimization, Function integration, reconstruction and approximation using rank-$1$ lattices

Uses Software

• CHEBINT

Cites Work

• Bivariate Lagrange interpolation at the Padua points: the generating curve approach
• Nontensorial Clenshaw-Curtis cubature
• New cubature formulae and hyperinterpolation in three variables
• The construction of cubature formulae for a family of integrals: A bifurcation problem
• Kubaturformeln mit minimaler Knotenzahl
• Blending methods for two classical integrals
• Minimal cubature formulae of degree 2k-1 for two classical functionals
• Polynomial interpolation and hyperinterpolation over general regions
• Cubature formula and interpolation on the cubic domain
• Construction of Algebraic Cubature Rules Using Polynomial Ideal Theory
• Is Gauss Quadrature Better than Clenshaw–Curtis?
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