Fast Evaluation of Radial Basis Functions: Methods for 4-Dimensional Polyharmonic Splines
by
Jon Cherrie
University of Canterbury
Coauthors: Rick Beatson (University of Canterbury), David Ragozin (University of Washington)

Radial Basis Functions (RBFs) are a popular choice for interpolation to non-gridded data in two or more dimensions. Due to the computational cost of direct evaluation, the use of RBFs is commonly perceived to be limited to small data sets. In this talk it will shown how the Fast Multipole Method of electrostatics may be applied to evaluate polyharmonic RBFs in four dimensions. A significant feature of the current work is the use of arguments based on the action of the group of non-zero quaternions. Use of this perspective allows a relatively efficient development of the relevant spherical harmonics and their properties.

Date received: June 13, 1999