2381/27598
Carl Richard Odell
Kernel Approximation on Compact Homogeneous Spaces
2012
University of Leicester
IR content
2012-11-28 10:06:45
article
https://leicester.figshare.com/articles/Kernel_Approximation_on_Compact_Homogeneous_Spaces/10120043
This thesis is concerned with approximation on compact homogeneous spaces.
The first part of the research involves a particular kind of compact homogeneous space, the hypersphere, S ͩˉ¹ embedded in R ͩ. It is a calculation of three integrals associated with approximation using radial basis functions, calculating the Fourier-Gegenbauer coefficients for two such functions. The latter part of the research is a calculation of an error bound for compact homogeneous spaces when interpolating with a G-invariant kernel, a generalisation of a result already known for spheres.