A Smooth and Compactly Supported Radial Function

Details A Smooth and Compactly Supported Radial Function A Smooth and Compactly Supported Radial Function

2006-01-09

arxiv.org/abs/math/0601161v1

Mathematics

Numerical Analysis

4 pages, radial basis functions, approximation theory

Scientific paper

In the field of radial basis functions mathematicians have been endeavouring to find infinitely differentiable and compactly supported radial functions. This kind of functions are extremely important for some reasons. First, its computational properties will be very good since it's compactly supported. Second, its error bound will converge very fast since it's infinitely differentiable. However there is hitherto no such functions which can be expressed in a simple form. This is a famous question. The purpose of this paper is to answer this question.

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