Computational methods for the fourier analysis of sparse high-dimensional functions
Autor(en): | Kämmerer, L. Kunis, S. Melzer, I. Potts, D. Volkmer, T. |
Stichwörter: | Fast Fourier transforms, Discretisation; Effective algorithms; High-dimensional; High-dimensional problems; Multivariate trigonometric polynomials, Fourier analysis | Erscheinungsdatum: | 2014 | Herausgeber: | Springer Verlag | Journal: | Lecture Notes in Computational Science and Engineering | Volumen: | 102 | Startseite: | 347 | Seitenende: | 363 | Zusammenfassung: | A straightforward discretisation of high-dimensional problems often leads to a curse of dimensions and thus the use of sparsity has become a popular tool. Efficient algorithms like the fast Fourier transform (FFT) have to be customised to these thinner discretisations and we focus on two major topics regarding the Fourier analysis of high-dimensional functions: We present stable and effective algorithms for the fast evaluation and reconstruction of multivariate trigonometric polynomials with frequencies supported on an index set I ⊂ 𝕫d. © Springer International Publishing Switzerland 2014. |
ISSN: | 14397358 | DOI: | 10.1007/978-3-319-08159-5_17 | Externe URL: | https://www.scopus.com/inward/record.uri?eid=2-s2.0-85000416259&doi=10.1007%2f978-3-319-08159-5_17&partnerID=40&md5=338d049415e819deed4ac3388846ed09 |
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geprüft am 17.05.2024