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Lp-error estimates for "shifted" surface spline interpolation on Sobolev space

Title
Lp-error estimates for "shifted" surface spline interpolation on Sobolev space
Authors
Yoon J.
Ewha Authors
윤정호
SCOPUS Author ID
윤정호scopus
Issue Date
2003
Journal Title
Mathematics of Computation
ISSN
0025-5718JCR Link
Citation
vol. 72, no. 243, pp. 1349 - 1367
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
The accuracy of interpolation by a radial basis function φ is usually very satisfactory provided that the approximant f is reasonably smooth. However, for functions which have smoothness below a certain order associated with the basis function φ, no approximation power has yet been established. Hence, the purpose of this study is to discuss the Lp-approximation order 1 ≤ p ≤ ∞) of interpolation to functions in the Sobolev space Wp k (Ω) with k > max(0, d/2 - d/p). We are particularly interested in using the "shifted" surface spline, which actually includes the cases of the multiquadric and the surface spline. Moreover, we show that the accuracy of the interpolation method can be at least doubled when additional smoothness requirements and boundary conditions are met.
DOI
10.1090/S0025-5718-02-01498-9
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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