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자연과학대학
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Some issues on interpolation matrices of locally scaled radial basis functions
Title
Some issues on interpolation matrices of locally scaled radial basis functions
Authors
Lee M.B.
;
Lee Y.J.
;
Sunwoo H.
;
Yoon J.
Ewha Authors
윤정호
SCOPUS Author ID
윤정호
Issue Date
2011
Journal Title
Applied Mathematics and Computation
ISSN
0096-3003
Citation
Applied Mathematics and Computation vol. 217, no. 10, pp. 5011 - 5014
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
Radial basis function interpolation on a set of scattered data is constructed from the corresponding translates of a basis function, which is conditionally positive definite of order m ≥ 0, with the possible addition of a polynomial term. In many applications, the translates of a basis function are scaled differently, in order to match the local features of the data such as the flat region and the data density. Then, a fundamental question is the non-singularity of the perturbed interpolation (N × N) matrix. In this paper, we provide some counter examples of the matrices which become singular for N ≥ 3, although the matrix is always non-singular when N = 2. One interesting feature is that a perturbed matrix can be singular with rather small perturbation of the scaling parameter. © 2010 Elsevier Inc. All rights reserved.
DOI
10.1016/j.amc.2010.11.040
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