Fast evaluation of polyharmonic splines in three dimensions

IMA Journal of Numerical Analysis

Volumn 27, Issue 3, 2007, Pages 427-450

  Beatson, R K ^a   Powell, M J D ^b   Tan, A M ^a  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Fast evaluation; Polyharmonic splines in three dimensions; Radial basis functions

Indexed keywords

FUNCTIONS; INTERPOLATION; PETROLEUM RESERVOIR EVALUATION;

FAST EVALUATION; FAST MULTIPOLE METHOD; MATRIX-VECTOR PRODUCTS; NEAR-FIELD EXPANSION; POLYHARMONIC SPLINES; RADIAL BASIS FUNCTIONS; SCATTERED DATA INTERPOLATION; THREE DIMENSIONS;

FUNCTION EVALUATION;

EID: 34547782169     PISSN: 02724979     EISSN: 14643642     Source Type: Journal    
DOI: 10.1093/imanum/drl027     Document Type: Article

References (13)

1. BARNES, J. & HUT, P. (1986) A hierarchical (N log N) force-calculation algorithm. Nature, 324, 446-449.
2. BEATSON, R. K. & GREENGARD, L. (1997) A short course on fast multipole methods. Wavelets, Multilevel Methods and Elliptic PDEs (M. Ainsworth, J. Levesley, W. A. Light & M. Marletta eds). Oxford: Clarendon Press, pp. 1-37.
3. BEATSON, R. K. & NEWSAM, G. N. (1992) Fast evaluation of radial basis functions: I. Comput. Math. Appl., 24, 7-19.
4. CARR, J. C., BEATSON, R. K., CHERRIE, J. B., MITCHELL, T. J., FRIGHT, W. R., MCCALLUM, B. C. & EVANS, T. R. (2001) Reconstruction and representation of 3D objects with radial basis functions. Computer Graphics SIGGRAPH 2001 Proceedings (E. Fiume ed.). New York, NY: ACM, pp. 67-76.
5. EPTON, M. A. & DEMBART, B. (1995) Multipole translation theory for the 3D Laplace and Helmholtz equations. SIAM J. Sci. Comput., 16, 865-897.
6. ERDELYI, A., MAGNUS, W., OBERHETTINGER, F. & TRICOMI, F. G. (1953) The Higher Transcendental Functions. The Bateman Manuscript Project, vol. 1. New York: McGraw-Hill.
7. FAUL, A. C., GOODSELL, G. & POWELL, M. J. D. (2005) A Krylov subspace algorithm for multiquadric interpolation in many dimensions. IMA J. Numer. Anal., 25, 1-24.
8. GREENGARD, L. ( 1988) The Rapid Evaluation of Potential Fields in Particle Systems. Cambridge, MA: MIT Press.
9. GREENGARD, L. & ROKHLIN, V. (1987) A fast algorithm for particle simulations. J. Comput. Phys., 73, 325-348.
10. GREENGARD, L. & ROKHLIN, V. (1988) Rapid evaluation of potential fields in three dimensions. Vortex Methods (C. Anderson & C. Greengard eds). Lecture Notes in Mathematics, vol. 1360. New York: Springer, pp. 121-141.
11. JACKSON, J. D. (1975) Classical Electrodynamics, 2nd edn. New York: Wiley.
12. POWELL, M. J. D. (1993) Truncated Laurent expansions for the fast evaluation of thin-plate splines. Numer. Algorithms, 5, 99-120.
13. PRESS, W. H., FLANNERY, B. P., TEUKOLSKY, S. A. & VETTERLING, W. T. (1988) Numerical Recipes in C. Cambridge: Cambridge University Press.