The L2-approximation order of surface spline interpolation
The L2-approximation order of surface spline interpolation
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DOI：
10.1090/s0025-5718-00-01301-6
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发表时间：
2001-01-01
影响因子：
2
通讯作者：
Johnson, MJ
中科院分区：
文献类型：
--
作者：
Johnson, MJ
证明了如果R-d的开有界域Omega子集有充分光滑的边界，且数据函数f充分光滑，则f与其曲面样条样条插值之间的误差的L-p(Omega)范数为O(Delta(Gammap+1/2))(1小于或等于p小于或等于无穷大)，其中Gamma(P)：=min{m，m-d/2+d/p}，m是指定曲面样条的整数参数.当p=2时，逼近阶的下界与已有的上界一致，因此我们得出曲面样条插值的L-2逼近阶为m+1/2。
We show that if the open, bounded domain Omega subset of R-d has a sufficiently smooth boundary and if the data function f is sufficiently smooth, then the L-p(Omega)-norm of the error between f and its surface spline interpolant is O(delta (gammap+1/2)) (1 less than or equal to p less than or equal to infinity), where gamma (p) := min{m, m - d/2 + d/p} and m is an integer parameter specifying the surface spline. In case p = 2, this lower bound on the approximation order agrees with a previously obtained upper bound, and so we conclude that the L-2-approximation order of surface spline interpolation is m + 1/2.