A fast algorithm for filtering and wavelet decomposition on the sphere

Electronic Transactions on Numerical Analysis

Volumn 16, Issue , 2003, Pages 70-93

  Böhme, Martin ^b   Potts, Daniel ^a  

^a UNIVERSITY OF LÜBECK   (Germany)

^b NONE

Author keywords

Associated Legendre functions; Fast discrete summation; Fast discrete transforms; Fast Fourier transform at nonequispaced knots; Spherical filter; Spherical Fourier transform; Spherical harmonics; Wavelets

Indexed keywords

EID: 1242294238     PISSN: 10689613     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (22)

1. G. BEYLKIN, On the fast Fourier transform of functions with singularities, Appl. Comput. Harmon. Anal., 2 (1995), pp. 363 - 381.
2. M. BÖHME, A fast algorithm for filtering and wavelet decomposition on the sphere. Diplomarbeit, Universität zu Lübeck, Report B-02-08, 2002.
3. J. P. BOYD, Chebyshev and Fourier Spectral Methods, Dover Press, New York, second ed., 2000.
4. J. DRISCOLL AND D. HEALY, Computing Fourier transforms and convolutions on the 2-sphere, Adv. in Appl. Math., 15 (1994), pp. 202 - 250.
5. A. DUTT, M. GU, AND V. ROKHLIN, Fast algorithms for polynomial interpolation, integration and differentiation, SIAM J. Numer. Anal., 33 (1996), pp. 1689 - 1711.
6. A. DUTT AND V. ROKHLIN, Fast Fourier transforms for nonequispaced data, SIAM J. Sci. Comput., 14 (1993), no. 6, pp. 1368 - 1393.
7. W. FREEDEN, T. GERVENS, AND M. SCHREINER, Constructive Approximation on the Sphere, Oxford University Press, Oxford, 1998.
8. D. FUNARO, Polynomial Approximation of Differential Equations, Springer-Verlag, Berlin, 1992.
9. D. HEALY, P. KOSTELEC, S. S. B. MOORE, AND D. ROCKMORE, FFTs for the 2-sphere - Improvements and variations, J. Fourier Anal. Appl., 9 (2003).
10. R. JAKOB-CHIEN AND B. K. ALPERT, A fast spherical filter with uniform resolution, J. Comput. Phys., 136 (1997), pp. 580 - 584.
11. S. KUNIS AND D. POTTS, NFFT, Softwarepackage, C subroutine library. (2002) http://www.math.uni-luebeck.de/potts/nfft.
12. W. MAGNUS AND F. OBERHETTINGER, Formeln und Sätze für die speziellen Funktionen der mathematischen Physik, Springer, Berlin, 1943.
13. M. J. MOHLENKAMP, A fast transform for spherical harmonics, J. Fourier Anal. Appl., 5 (1999), pp. 159 - 184.
14. D. POTTS AND G. STEIDL, Fast summation at nonequispaced knots by NFFTs, SIAM J. Sci. Comput., (to appear).
15. D. POTTS, G. STEIDL, AND M. TASCHE, Kernels of Spherical Harmonics and Spherical Frames, in Advanced Topics in Multivariate Approximation, F. Fontanella, K. Jetter, and P.-J. Laurent, eds., World Scientific Publ., Singapore, 1996, pp. 287 - 301.
16. _, Fast and stable algorithms for discrete spherical Fourier transforms, Linear Algebra Appl., 275 (1998), pp. 433 - 450.
17. _, Fast Fourier transforms for nonequispaced data: A tutorial, in Modern Sampling Theory: Mathematics and Applications, J. J. Benedetto and P. J. S. G. Ferreira, eds., Boston, 2001, Birkhäuser, pp. 247 - 270.
18. G. STEIDL, A note on fast Fourier transforms for nonequispaced grids, Adv. Comput. Math., 9 (1998), pp. 337 - 353.
19. R. SUDA AND M. TAKAMI, A fast spherical harmonics transform algorithm, Math. Comp., 71 (2002), no. 238, pp. 703 - 715, (electronic).
20. P. N. SWARZTRAUBER AND W. F. SPOTZ, Generalized discrete spherical harmonic transforms, J. Comput. Phys., 159 (2000), pp. 213 - 230.
21. _, A performance comparison of associated Legendre projections, J. Comput. Phys., 168 (2001), pp. 339 - 355.
22. N. YARVIN AND V. ROKHLIN, A generalized one-dimensional fast multipole method with application to filtering of spherical harmonics, J. Comput. Phys., 147 (1998), pp. 549 - 609.