Fast evaluation of radial basis functions : theory and application.
Degree GrantorUniversity of Canterbury
Degree NameDoctor of Philosophy
Radial Basis Functions (RBFs) have proven to be successful interpolants to scattered data. However, the perceived high computational costs for fitting and evaluating the RBFs associated with large data sets have hindered their application to many real world problems. This thesis is concerned with the "fast" evaluation of RBFs: the O(N2) process of evaluation at all centres is reduced to O(N log N) or even O(N). The required theory is developed for polyharmonic RBFs in 4-dimensions and for multiquadric RBFs in arbitrary dimensions. These methods are applied to fit surfaces to scattered data containing many tens of thousands of points.