On the stability of the hyperbolic cross discrete Fourier transform

DOI10.1007/s00211-010-0322-7zbMath1213.65159OpenAlexW2023767122MaRDI QIDQ629898

Lutz Kämmerer, Stefan Kunis

Publication date: 10 March 2011

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-010-0322-7

zbMATH Keywords

stabilitynumerical experimentscondition numberspectral normBoolean sum decompositionhyperbolic cross discrete Fourier transforminverse Fourier matrixmultidimensional discrete Fourier transformsparse grid approximation

Mathematics Subject Classification ID

Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42B10) Numerical computation of matrix norms, conditioning, scaling (65F35) Numerical methods for discrete and fast Fourier transforms (65T50) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (12)

Trigonometric interpolation on lattice grids ⋮ Sparse high-dimensional FFT based on rank-1 lattice sampling ⋮ Constructive subsampling of finite frames with applications in optimal function recovery ⋮ On the fundamental conjecture of HDMR: a Fourier analysis approach ⋮ Multiple rank-1 lattices as sampling schemes for multivariate trigonometric polynomials ⋮ Interpolation lattices for hyperbolic cross trigonometric polynomials ⋮ Reconstruction and collocation of a class of non-periodic functions by sampling along tent-transformed rank-1 lattices ⋮ Constructing spatial discretizations for sparse multivariate trigonometric polynomials that allow for a fast discrete Fourier transform ⋮ 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 ⋮ Multivariate Vandermonde matrices with separated nodes on the unit circle are stable

Uses Software

• NHCFFT

Cites Work

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• Fouriertransform on sparse grids with hierarchical bases
• Fourier transform on sparse grids: Code design and the time dependent Schrödinger equation
• Nonequispaced Hyperbolic Cross Fast Fourier Transform
• A Class of Periodic Function Spaces and Interpolation on Sparse Grids
• Sparse grids
• Data mining with sparse grids

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