Ill-conditioning and numerical stability in radial basis functions (RBFs) using frame theory

Seminar series

Numerical Analysis Group Internal Seminar

Date

Tue, 09 May 2017
14:30

Location

Speaker

Cécile Piret

Organisation

Michigan Technological University

We analyse the numerical approximation of functions using radial basis functions in the context of frames. Frames generalize the notion of a basis by allowing redundancy, while being restricted by a so-called frame condition. The theory of numerical frame approximations allows the study of ill-conditioning, inherently due to their redundancy, and suggests discretization techniques that still offer numerical stability to machine precision. We apply the theory to radial basis functions.