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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
윤정호scopus
Issue Date
2011
Journal Title
Applied Mathematics and Computation
ISSN
0096-3003JCR Link
Citation
vol. 217, no. 10, pp. 5011 - 5014
Indexed
SCIE; SCOPUS WOS scopus
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
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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