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Open Access Green as soon as Postprint is submitted to ZB.
On the stability of the hyperbolic cross discrete Fourier transform.
Numer. Math. 117, 581-600 (2011)
A straightforward discretisation of problems in high dimensions often leads to an exponential growth in the number of degrees of freedom. Sparse grid approximations allow for a severe decrease in the number of used Fourier coefficients to represent functions with bounded mixed derivatives and the fast Fourier transform (FFT) has been adapted to this thin discretisation. We show that this so called hyperbolic cross FFT suffers from an increase of its condition number for both increasing refinement and increasing spatial dimension.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Trigonometric approximation; Hyperbolic cross; Sparse grid; Fast Fourier transform
ISSN (print) / ISBN
0029-599x
e-ISSN
0945-3245
Journal
Numerische Mathematik
Quellenangaben
Volume: 117,
Issue: 3,
Pages: 581-600
Publisher
Springer
Publishing Place
Berlin ; Heidelberg [u.a.]
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Biomathematics and Biometry (IBB)