Bengt Fornberg
Dept. of Applied Mathematics
University of Colorado
Boulder, Colorado, USA
Radial basis functions (RBFs) were first proposed around 1970 as a method for interpolating scattered 2-D data. More recently, both our knowledge about RBFs and their range of applications have grown tremendously. They easily generalize to multiple dimensions, handle irregular domains, and can be spectrally accurate both for interpolation and for solving PDEs. Following a summary of some basics properties of RBF interpolants, we will focus on some new computational algorithms for the resulting linear systems, and also on new opportunities opened up by an improved understanding of the Runge phenomenon for RBFs.