Fast convolution with radial kernels at nonequispaced knots

Numerische Mathematik

Volumn 98, Issue 2, 2004, Pages 329-351

  Potts, Daniel ^a   Steidl, Gabriele ^b   Nieslony, Arthur ^b  

^a UNIVERSITY OF LÜBECK   (Germany)

^b UNIVERSITY OF MANNHEIM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4544236321     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00211-004-0538-5     Document Type: Article

References (30)

1. MadMax Optics, FMM Toolbox™. http://www.madmaxoptics.com, 2003
2. Beatson, R. K., Light, W. A.: Fast evaluation of radial basis functions: methods for 2-dimensional polyharmonic splines. IMA J. Numer. Anal. 17, 343-372 (1997)
3. Beatson, R. K., Newsam, G. N.: Fast evaluation of radial basis functions: Moment based methods. SIAM J. Sci. Comput. 19, 1428-1449 (1998)
4. Beylkin, G.: On the fast Fourier transform of functions with singularities. Appl. Comput. Harmon. Anal. 2, 363-381 (1995)
5. Böhme, M., Potts, D.: A fast algorithm for filtering and wavelet decomposition on the sphere. Electron. Trans. Numer. Anal. 16, 70-92 (2003)
6. Broadie, M., Yamamoto, Y.: Application of the fast Gauss transform to option pricing, Management Science 49, 1071-1088 (2003)
7. n. SIAM J. Sci. Comput. 23, 1549-1571 (2002)
8. Duchon, J.: Fonctions splines et vecteurs aleatoires. Technical report, Seminaire d'Analyse Numerique, Universite Scientifiqae et Medicale, Grenoble, 1975
9. Duijndam, A. J. W., Schonewille, M. A.: Nonuniform fast Fourier transform. Geophysics 64, 539-551 (1999)
10. Dutt, A., Rokhlin, V.: Fast Fourier transforms for nonequispaced data. SIAM J. Sci. Stat. Comput. 14, 1368-1393 (1993)
11. Elgammal, A., Duraiswami, R., Davis, L. S.: Efficient non-parametric adaptive color modeling using fast Gauss transform. Technical report, The Univ. of Maryland, 2001
12. Fessler, J., Sutton, B.: NUFFT - nonuniform FFT toolbox for Matlab. http://www.eecs.umich.edu/~fessler/code/index.html, 2002
13. Fourmont, K.: Schnelle Fourier-Transformation bei nichtäquidistanten Gittern und tomographische Anwendungen. Dissertation, Universität Münster, 1999
14. Frigo, M., Johnson, S. G.: FFTW, a C subroutine library, http://www.fftw.org/
15. Goreinov, S. A., Tyrtyshnikov, E. E., Yeremin, E. E.: Matrix-free iterative solution strategies for large dense systems. Numer. Linear Algebra Appl. 4, 273-294 (1997)
16. Greengard, L.: The Rapid Evaluation of Potential Fields in Particle Systems. MIT Press, Cambridge, 1988
17. Greengard, L., Lin, P.: Spectral approximation of the free-space heat kernel. Appl. Comput. Harmon. Anal. 9, 83-97 (2000)
18. Greengard, L., Rokhlin, V.: A fast algorithm for particle simulations. J. Comput. Phys. 73, 325-348 (1987)
19. Greengard, L., Strain, J.: The fast Gauss transform. SIAM J. Sci. Stat. Comput. 12, 79-94 (1991)
20. Greengard, L., Sun, X.: A new version of the fast Gauss transform. Doc. Math. J. DMV 3, 575-584 (1998)
21. Hackbusch, W.: A sparse matrix arithmetic based on H-matrices, Part I: introduction to H-matrices. Computing 62, 89-108 (1999)
22. Hackbusch, W., Nowak, Z. P.: On the fast matrix multiplication in the boundary element method by panel clustering. Numer. Math. 54, 463-491 (1989)
23. Kunis, S., Potts, D.: NFFT, Softwarepackage, C subroutine library. http://www.math.uni-luebeck.de/potts/nfft, 2002
24. Potts, D., Steidl, G.: Fast summation at nonequispaced knots by NFFTs. SIAM J. Sci. Comput. 24, 2013-2037 (2003)
25. Potts, D., Steidl, G., Tasche, M.: Trigonometric preconditioners for block Toeplitz systems. In G. Nümberger, J. W. Schmidt, and G. Walz, editors, Multivariate Approximation and Splines, pages 219-234, Birkhäuser, Basel, 1997
26. Potts, D., Steidl, G., Tasche, M.: Fast Fourier transforms for nonequispaced data: A tutorial. In J. J. Benedetto and P. J. S. G. Ferreira, editors. Modern Sampling Theory: Mathematics and Applications, pages 247-270, Boston, 2001. Birkhäuser
27. Steidl, G.: A note on fast Fourier transforms for nonequispaced grids. Adv. Comput. Math. 9, 337-353 (1998)
28. Sun, X., Pitsianis, N. P.: A matrix version of the fast multipole method. SIAM Rev. 43, 289-300 (2001)
29. Tyrtyshnikov, E. E.: Mosaic-skeleton approximations. Calcolo, 33, 47-57 (1996)
30. Yarvin, N., Rokhlin, V.: An improved fast multipole algorithm for potential fields on the line. SIAM J. Numer. Anal. 36, 629-666 (1999)