Johnson, M.J. (1998) On the error in surface spline interpolation of a compactly supported function. Preprint, Kuwait University  Home/Search   Document Details and Download   Summary   Related Articles

....be checked that the same rate of decay is usual for larger values of p or even for C 1 bump functions f . However, the univariate natural spline case (d = 1, fl 2 2N 1) shows that a positive answer to the question above is sometimes possible. Much insight has been obtained recently by Johnson [11] for the multivariable case in which fl is a positive integer such that fl d is even, and for the version of the surface spline interpolation method that uses Pi d (fl d) 2 Gamma1 instead of Pi d m in the definition of S h . His approach is based on the best approximation property that ....

....1.904956 1.904987 Table 2: Evaluations of the Lebesgue constant for d = fl = 2. Remark 5 We note that all the results of the present paper remain valid whenever the polynomial space Pi d m used in the definition of S h is replaced by Pi d k , for k m. As mentioned in Section 1, Johnson [11] has recently obtained the convergence rate (3.17) by different means in the scattered data case, for the variant of the surface spline interpolation scheme that uses Pi d (fl d) 2 Gamma1 instead of Pi d m in the definition of S h . Remark 6 Our approach based on the Lebesgue inequality ....

Johnson, M.J. (1998) On the error in surface spline interpolation of a compactly supported function. Preprint, Kuwait University

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