Fast evaluation of radial basis functions: Moment-based methods

SIAM Journal on Scientific Computing

Volumn 19, Issue 5, 1998, Pages 1428-1449

  Beatson, R K ^a   Newsam, G N ^b  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

^b DEFENCE SCIENCE AND TECHNOLOGY ORGANISATION   (Australia)

Author keywords

Fast evaluation; Fast multiple method; Moment based method; Radial basis functions

Indexed keywords

EID: 0001332214     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827595293569     Document Type: Review

References (19)

1. B. K. ALPERT AND V. ROKHLIN, A fast algorithm for the evaluation of Legendre expansions, SIAM J. Sci. Comput., 12 (1991), pp. 158-179.
2. B. K. ALPERT, G. BEYLKIN, R. COIFMAN, AND V. ROKHLIN, Wavelet like bases for the fast solution of second-kind integral equations, SIAM J. Sci. Comput., 14 (1993), pp. 159-184.
3. 2 for the sparse representation of integral operators, SIAM J. Math. Anal., 24 (1993), pp. 246-262.
4. A. W. APPEL, An efficient program for many body simulations, SIAM J. Sci. Statist. Comput., 6 (1985), pp. 85-103.
5. J. BARNES AND P. HUT, A hierarchical O(N log N) force-calculation algorithm, Nature, 324 (1986), pp. 446-449.
6. R. K. BEATSON AND W. A. LIGHT, Fast evaluation of radial basis functions: Methods for 2-dimensional polyharmonic splines, IMA J. Numer. Anal., 17 (1997), pp. 343-372.
7. R. K. BEATSON AND G. N. NEWSAM, Fast evaluation of radial basis functions: I, Comput. Math. Appl., 24 (1992), pp. 7-19.
8. G. BEYLKIN, R. COIFMAN AND V. ROKHLIN, Fast wavelet transforms and numerical algorithms: I, Comm. Pure Appl. Math., 44 (1991), pp. 141-183.
9. J. CARRIER, L. GREENGARD AND V. ROKHLIN, A fast adaptive multipole algorithm for particle simulations, SIAM J. Sci. Comput., 9 (1988), pp. 669-686.
10. L. GREENGARD AND V. ROKHLIN, A fast algorithm for particle simulations, J. Comput. Phys., 73 (1987), pp. 325-348.
11. L. GREENGARD, The Rapid Evaluation of Potential Fields in Particle Systems, MIT Press, Cambridge, MA, 1988.
12. L. GREENGARD AND V. ROKHLIN, On the Efficient Implementation of the Fast Multipole Algorithm, Department of Computer Science Report 602, Yale University, New Haven, CT, 1988.
13. L. GREENGARD AND J. STRAIN, The fast Gauss transform, SIAM J. Sci. Comput., 2 (1991), pp. 79-94.
14. W. HACKBUSH AND Z. K. NOWAK, On the fast matrix multiplication in the boundary element method by panel clustering, Numer. Math., 54 (1989), pp. 463-491.
15. G. G. LORENTZ, Approximation of Functions, Holt, Rinehart and Winston, New York, 1966.
16. M. J. D. POWELL, Truncated Laurent expansions for the fast evaluation of thin plate splines, Algorithms for Approx., 5 (1993), pp. 99-120.
17. T. J. RIVLIN, The Chebyshev Polynomials, Wiley-Interscience, New York, 1974.
18. J. STRAIN, The fast Gauss transform with variable scales, SIAM J. Sci. Comput., 12 (1991), pp. 1131-1139.
19. F. ZHAO, An O(N) Algorithm for 3-Dimensional N-Body Simulations, Technical Report 995, Artificial Intelligence Laboratory, MIT, Cambridge, MA, 1987.