Fast evaluation of radial basis functions: Methods for two-dimensional polyharmonic splines

IMA Journal of Numerical Analysis

Volumn 17, Issue 3, 1997, Pages 343-372

  Beatson, R K ^a   Light, W A ^b  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

^b UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS;

FAST MULTIPOLE METHOD; FASTER CONVERGENCE; NUMERICAL EXPERIMENTS; POLYHARMONIC SPLINES; RADIAL BASIS FUNCTIONS; RATE OF CONVERGENCE; SERIES APPROXIMATIONS; THIN PLATE SPLINE;

FUNCTION EVALUATION;

EID: 0031488175     PISSN: 02724979     EISSN: None     Source Type: Journal    
DOI: 10.1093/imanum/17.3.343     Document Type: Article

References (12)

1. AMODEI, L., & BENBOURHIM, M. N. 1991 A vector spline approximation. J. Approx. Theory 67, 51-79.
2. BEATSON, R. K., & NEWSAM, G. N. 1992 Fast evaluation of radial basis functions, I. Comput. Math. Applic. 24, 7-19.
3. BEATSON, R. K. 1996 Thin: a collection of routines for fast computation with radial basis functions. In preparation.
4. BUHMANN, M. D. 1993 New developments in the theory of radial basis interpolation. Multivariate Approximation: from CAGD to Wavelets (K. Jetter and F. I. Utreras, eds). Singapore: World Scientific, pp 35-75.
5. CHURCHILL, R. V., & BROWN, J. W. 1984 Complex Variables and Applications 4th edn. New York: McGraw Hill.
6. GREENGARD, L., & ROKHLIN, V. 1987 A fast algorithm for particle simulations. J. Comput. Phys. 73, 325-348.
7. LIGHT, W. A. 1992 Some aspects of radial basis function approximation. Approximation Theory, Spline Functions and Applications (S. P. Singh, ed). Dordrecht: Kluwer, pp 163-190.
8. POWELL, M. J. D. 1992 The theory of radial basis function approximation in 1990. Advances in Numerical Analysis II: Wavelets, Subdivision Algorithms and Radial Functions (W. Light, ed). Oxford: Oxford University Press, pp 105-210.
9. POWELL, M. J. D. 1993 Truncated Laurent expansions for the fast evaluation of thin plate splines. Algorithms Approx. 5, 99-120.
10. RABUT, C. 1990 B-splines polyharmoniques cardinales: interpolation, quasi-interpolation, filtrage. Thèse d'Etat, Université de Toulouse.
11. SUTER, D. 1992 Efficient recovery of "Time to Crash" from optic flow. Technical Report, Department of Electrical and Computer Systems Engineering, Monash University.
12. ZHAO, F. 1987 An O(N) algorithm for 3-dimensional N-body simulations. Technical Report 995, Artificial Intelligence Laboratory, MIT.