The Mathematical Institute, University of Oxford, Eprints Archive

Compactly supported radial basis functions: How and why?

Zhu, Shengxin (2012) Compactly supported radial basis functions: How and why? Technical Report. SIAM. (Submitted)

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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.

Item Type:Technical Report (Technical Report)
Subjects:O - Z > Real functions
O - Z > Special functions
A - C > Approximations and expansions
D - G > General
H - N > Mathematics education
H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1570
Deposited By:Lotti Ekert
Deposited On:26 Jul 2012 09:16
Last Modified:26 Jul 2012 09:16

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