AMCA: The Asymptotics of Fekete-type Points for Univariate Radial Basis Interpolation by Len Bos

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Surface Approximation and Visualisation II
February 19-22, 2002
New Zealand Approximation Theory Group
Westport, New Zealand

Organizers
Rick Beatson, Keith Unsworth, Shayne Waldron

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The Asymptotics of Fekete-type Points for Univariate Radial Basis Interpolation
by
Len Bos
University of Calgary

Suppose that 0 <= x₁ < x₂ < ... < x_n <= 1 and g : [0, 1] --> R is some function. Consider the radial basis interpolation matrix for these points, i.e.

M_n:=[g(|x_i-x_j|)].

We show, that for a large class of functions g, the points which maximize the determinant of M_n are asymptotically equally spaced.

Date received: February 4, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # caie-13.