Multivariate Approximation and High-Dimensional Sparse FFT Based on Rank-1 Lattice Sampling
Seiten
2017
Universitätsverlag Chemnitz
978-3-96100-020-3 (ISBN)
Universitätsverlag Chemnitz
978-3-96100-020-3 (ISBN)
- Titel ist leider vergriffen;
keine Neuauflage - Artikel merken
In this work, the fast evaluation and reconstruction of multivariate trigonometric polynomials with frequencies supported on arbitrary index sets of finite cardinality is considered, where rank-1 lattices are used as spatial discretizations. The approximation of multivariate smooth periodic functions by trigonometric polynomials is studied, based on a one-dimensional FFT applied to function samples. The smoothness of the functions is characterized via the decay of their Fourier coefficients, and various estimates for sampling errors are shown, complemented by numerical tests for up to 25 dimensions. In addition, the special case of perturbed rank-1 lattice nodes is considered, and a fast Taylor expansion based approximation method is developed.
One main contribution is the transfer of the methods to the non-periodic case. Multivariate algebraic polynomials in Chebyshev form are used as ansatz functions and rank-1 Chebyshev lattices as spatial discretizations. This strategy allows for using fast algorithms based on a one-dimensional DCT. The smoothness of a function can be characterized via the decay of its Chebyshev coefficients. From this point of view, estimates for sampling errors are shown as well as numerical tests for up to 25 dimensions.
A further main contribution is the development of a high-dimensional sparse FFT method based on rank-1 lattice sampling, which allows for determining unknown frequency locations belonging to the approximately largest Fourier or Chebyshev coefficients of a function.
One main contribution is the transfer of the methods to the non-periodic case. Multivariate algebraic polynomials in Chebyshev form are used as ansatz functions and rank-1 Chebyshev lattices as spatial discretizations. This strategy allows for using fast algorithms based on a one-dimensional DCT. The smoothness of a function can be characterized via the decay of its Chebyshev coefficients. From this point of view, estimates for sampling errors are shown as well as numerical tests for up to 25 dimensions.
A further main contribution is the development of a high-dimensional sparse FFT method based on rank-1 lattice sampling, which allows for determining unknown frequency locations belonging to the approximately largest Fourier or Chebyshev coefficients of a function.
| Erscheinungsdatum | 14.07.2017 |
|---|---|
| Zusatzinfo | Illustrationen |
| Verlagsort | Chemnitz |
| Sprache | englisch |
| Maße | 148 x 210 mm |
| Gewicht | 258 g |
| Themenwelt | Mathematik / Informatik ► Mathematik |
| Schlagworte | DCT • DFT • Diskrete Fourier-Transformation • Drawing Completion Test • FFT • komponentenweise Konstruktion • Multivariate approximation • Rang-1-Gitter • Schnelle Fourier-Transformation • unbekannte Frequenzindexmenge |
| ISBN-10 | 3-96100-020-4 / 3961000204 |
| ISBN-13 | 978-3-96100-020-3 / 9783961000203 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
Mehr entdecken
aus dem Bereich
aus dem Bereich
Von Logik und Mengenlehre bis Zahlen, Algebra, Graphen und …
Buch | Softcover (2024)
De Gruyter Oldenbourg (Verlag)
CHF 104,90
Grundlagen für das Bachelor-Studium
Buch | Hardcover (2023)
Hanser (Verlag)
CHF 55,95
Analysis und Lineare Algebra mit Querverbindungen
Buch | Hardcover (2022)
Springer Spektrum (Verlag)
CHF 97,95
