Math 594A: Special Topics in Numerical Analysis:
Introduction to Approximations and Fast Computations on Spheres and Euclidean
Spaces
David Ragozin
Autumn 2000, Monday/Wednesday 3:30-4:45
General Topics: Rotation or translation operators on Sd
or
Rd+1 provide tools which can greatly simplify
the study and construction of approximation processes on these spaces.
This course will consider polynomial and variational spline approximation
processes on these spaces. General results considered will include
relations between order of approximation and smoothness (Jackson-Bernstein
theorems), error estimates for variational spline approximation, particularly
for radial basis functions, and group invariance approaches to fast computational
methods for polyharmonic splines.