Interpolation lattices for hyperbolic cross trigonometric polynomials

DOI10.1016/j.jco.2011.05.002zbMath1335.65105OpenAlexW1990197703MaRDI QIDQ657653

Stefan Kunis, Lutz Kämmerer, Daniel Potts

Publication date: 10 January 2012

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2011.05.002

zbMATH Keywords

sparse gridtrigonometric polynomialsmultivariate numerical integrationhyperbolic cross fast Fourier transforminterpolation lattices

Mathematics Subject Classification ID

Trigonometric interpolation (42A15) Numerical methods for discrete and fast Fourier transforms (65T50) Numerical quadrature and cubature formulas (65D32) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (11)

Trigonometric interpolation on lattice grids ⋮ Rhodonea curves as sampling trajectories for spectral interpolation on the unit disk ⋮ Tight error bounds for rank-1 lattice sampling in spaces of hybrid mixed smoothness ⋮ On computing high-dimensional Riemann theta functions ⋮ On the fundamental conjecture of HDMR: a Fourier analysis approach ⋮ Multiple rank-1 lattices as sampling schemes for multivariate trigonometric polynomials ⋮ Reconstruction and collocation of a class of non-periodic functions by sampling along tent-transformed rank-1 lattices ⋮ Function integration, reconstruction and approximation using rank-$1$ lattices ⋮ Fast Discrete Fourier Transform on Generalized Sparse Grids ⋮ Approximation of multivariate periodic functions by trigonometric polynomials based on sampling along rank-1 lattice with generating vector of Korobov form ⋮ Approximation of multivariate periodic functions by trigonometric polynomials based on rank-1 lattice sampling

Uses Software

• NHCFFT
• NFFT
• NFFT3

Cites Work

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• Nonequispaced Hyperbolic Cross Fast Fourier Transform
• Parameters for Integrating Periodic Functions of Several Variables
• Lattice Rules by Component Scaling
• A Class of Periodic Function Spaces and Interpolation on Sparse Grids
• Minimal cubature formulae of trigonometric degree
• Sparse grids

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