PIMS / AMI Seminar: Martin Buhmann

In this talk we give a review of the approach to multivariable interpolation and approximation using radial basis functions. They are most popular in theory and applications because they provide approximants and interpolants in any space dimension, and for any distribution of data points. We focus on an introduction for a general audience of interpolation (as compared to the alternative approach of quasi-interpolation as studied recently by Feng Dai and the speaker) using the example of multiquadric radial basis function which has a parameter whose value can be modified to adapt to the data. We study especially the effects of changing this parameter.