Department of Mathematics
Recent developments in radial basis functions interpolation with applications to the geosciences.
Grady Wright
University of Utah
Radial basis functions (RBFs) are a powerful tool for interpolating/approximating scattered data. They easily generalize to multiple dimensions, handle arbitrarily scattered data, and can be spectrally accurate both for interpolation and for numerically solving partial differential equations (PDEs). Since their discovery in the early 1970s, both the knowledge about RBFs and their range of applications have grown tremendously. Some of these more recent applications include geophysics, neural networks, pattern recognition, and graphics and imaging. We will first review the basic properties of RBF interpolation and briefly discuss some recent computational algorithms for the resulting linear systems. We will then focus on two new RBF approaches for numerically solving PDEs. The first is a spectral collocation method for PDEs arising in climate modeling on the surface of a sphere. The second is on a local finite difference-type technique for PDEs on irregularly shaped domains.
All interested persons are welcome.
The talk will be accessible to upper class students.