The high-level error bound for shifted surface spline interpolation

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Luh, Lin-Tian;
(2006)
  • Subject: 41A05,41A15,41A25,41A30,41A63,65D10 | Mathematics - Numerical Analysis

Radial function interpolation of scattered data is a frequently used method for multivariate data fitting. One of the most frequently used radial functions is called shifted surface spline, introduced by Dyn, Levin and Rippa in \cite{Dy1} for $R^{2}$. Then it's extended... View more
  • References (21)
    21 references, page 1 of 3

    [1] M. Abramowitz and I. Stegun, A Handbook of Mathematical Functions, Dover Publications, New York, 1970.

    [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.

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