Compactly supported radial basis functions: How and why?

This is the latest version of this item.

Abstract

The use of radial basis functions have attracted increasing attention in recent years as an elegant scheme for high-dimensional scattered data approximation, an practical method for machine learning, one of the foundations of mesh-free methods, an alternative way to construct higher order methods for solving partial dierential equations (PDEs), an emerging method for solving PDEs on surfaces, a novel method for mesh repair and so on. All these applications share one mathematical foundation: high dimensional approximation/interpolation. This paper explains why radial basis functions are preferred to multi-variate polynomials for scattered data approximation in high-dimensional space; and gives a brief description on how to construct the most commonly used compactly supported radial basis functions. Without sophisticated mathematics, one can construct a compactly supported (radial) basis function with required smoothness according to procedures described here. Short programs and tables for compactly supported radial basis functions are supplied.

Available Versions of this Item

• Compactly supported radial basis functions: How and why? (deposited 05 May 2012 08:19)
  • Compactly supported radial basis functions: How and why? (deposited 26 Jul 2012 09:16) [Currently Displayed]