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Convergence of increasingly flat radial basis interpolants to polynomial interpolants

Title
Convergence of increasingly flat radial basis interpolants to polynomial interpolants
Authors
Lee Y.J.Yoon G.J.Yoon J.
Ewha Authors
윤정호이연주
SCOPUS Author ID
윤정호scopus
Issue Date
2007
Journal Title
SIAM Journal on Mathematical Analysis
ISSN
0036-1410JCR Link
Citation
vol. 39, no. 2, pp. 537 - 553
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
In this paper, we study the convergence behavior of interpolants by smooth radial basis functions to polynomial interpolants in ℝd as the radial basis functions are scaled to be increasingly flat. Larsson and Fornberg [Comput. Math. Appl., 49 (2005), pp. 103-130] conjectured a sufficient property for this convergence, and they also conjectured that Bessel radial functions do not satisfy this property. First, in the case of positive definite radial functions, we prove both conjectures by Larsson and Fornberg for the convergence of increasingly flat radial function interpolants. Next, we extend the results to the case of conditionally positive definite radial functions of order m > 0. © 2007 Society for Industrial and Applied Mathematics.
DOI
10.1137/050642113
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자연과학대학 > 수학전공 > Journal papers
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