publication . Preprint . 2006

The high-level error bound for shifted surface spline interpolation

Luh, Lin-Tian;
Open Access English
  • Published: 08 Jan 2006
Abstract
Comment: 14 pages, radial basis functions, approximation theory. arXiv admin note: text overlap with arXiv:math/0601158
Subjects
free text keywords: Mathematics - Numerical Analysis, 41A05,41A15,41A25,41A30,41A63,65D10
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21 references, page 1 of 2

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[2] M.D. Buhmann, New Development in the Theory of Radial Basis Functions Interpolation, Multivariate Approximation: From CAGD to Wavelets(K. Jetter, F.I. Utreras eds.), World Sciectific, Singapore, (1993), 35-75.

[3] J. Duchon, Sur l'erreur d'interpolation des fonctions de plusiers variables par les Dm-splines, RAIRO Analyse numerique 12(1978), 325-334.

[4] N. Dyn, D. Levin, S. Rippa, Numerical procedures for global surface fitting of scattered data by radial functions, SIAM J. Sci. and Sta. Computing 7(1986), 639-659.

[5] N. Dyn, Interpolation and Approximation by Radial and Related Functions, Approximation Theory VI,(C.K. Chui, L.L. Schumaker and J. Ward eds.), Academic press,(1989), 211-234.

[6] I.M. Gelfand and G.E. Shilov, Generalized Functions, Vol.1, Academic Press, 1964.

[7] Lin-Tian Luh, The Equivalence Theory of Native Space, Approx. Theory and its Applications, 2001, 17:1, 76-96.

[8] Lin-Tian Luh, The Embedding Theory of Native Spaces, Approx. Theory and its Applications, 2001, 17:4, 90-104.

[9] Lin-Tian Luh, On Wu and Schaback's Error Bound, to appear.

[10] Lin-Tian Luh, The completeness of Function Spaces, to appear.

[11] Lin-Tian Luh, On the High-Level Error Bound for Multiquadric and Inverse Multiquadric Interpolations, to appear.

[12] W.R. Madych and S.A. Nelson, Multivariate interpolation and conditionally positive definite function, Approx. Theory Appl. 4, No. 4(1988), 77-89.

[13] W.R. Madych and S.A. Nelson, Multivariate interpolation and conditionally positive definite function, II, Math. Comp. 54(1990), 211-230.

[14] W.R. Madych and S.A. Nelson, Bounds on Multivariate Polynomials and Exponential Error Estimates for Multiquadric Interpolation, J. Approx. Theory 70, 1992, 94-114. [OpenAIRE]

[15] M.J.D. Powell, The Theory of Radial Basis Functions Approximation in 1990, Advances in Numerical Analysis Vol.II:Wavelets, Subdivision Algorithms and Radial Basis Functions(W.A. Light ed.), Oxford University Press,(1992), 105-210.

21 references, page 1 of 2
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