The Mathematical Institute, University of Oxford, Eprints Archive

Convexity and solvability for compactly supported radial basis functions with different shapes

Zhu, S and Wathen, A. J. (2014) Convexity and solvability for compactly supported radial basis functions with different shapes. SISC . (Submitted)

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Abstract

It is known that interpolation with radial basis functions of the same shape can guarantee a non-singular interpolation matrix, whereas little is known when one uses various shapes. In this paper, we prove that a class of compactly supported radial basis functions are convex on a certain region; based on this local convexity and ready local geometrical property of the interpolation points, we construct a sufficient condition which guarantees diagonally dominant interpolation matrices for radial basis functions interpolation with various shapes. The proof is constructive and can be used to design algorithms directly. Real applications from 3D surface reconstruction are used
to verify the results.

Item Type:Article
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1819
Deposited By: Helen Taylor
Deposited On:12 Mar 2014 08:45
Last Modified:29 May 2015 19:30

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