Recent developments in error estimates for scattered-data interpolation via radial basis functions

被引：0
作者：
Francis J. Narcowich
机构：
[1] Texas A&M University,Department of Mathematics
来源：
Numerical Algorithms | 2005年 / 39卷
关键词：
interpolation; scattered data; radial basis functions; band-limited functions; error estimates;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Error estimates for scattered data interpolation by “shifts” of a positive definite function for target functions in the associated reproducing kernel Hilbert space (RKHS) have been known for a long time. However, apart from special cases where data is gridded, these interpolation estimates do not apply when the target functions generating the data are outside of the associated RKHS, and in fact until very recently no estimates were known in such situations. In this paper, we review these estimates in cases where the underlying space is Rn and the positive definite functions are radial basis functions (RBFs).
引用
收藏
页码：307 / 315
页数：8
相关论文
共 24 条
  • [1] Buhmann M.D.(1990)Multivariate cardinal interpolation with radial basis functions Constr. Approx. 6 225-255
  • [2] de Boor C.(1994)Approximation from shift-invariant subspaces of Trans. Amer. Math. Soc. 341 787-806
  • [3] DeVore R.(1978)( RAIRO Anal. Numér. 12 325-334
  • [4] Ron A.(1943)) Ann. Math. 44 330-337
  • [5] Duchon J.(1988)Sur l’erreur d’interpolation des fonctions de plusieurs variables par les Approx. Theory Appl. 4 77-79
  • [6] Erdős P.(1990)-splines Math. Comp. 54 211-230
  • [7] Madych W.R.(2002)On some convergence properties of the interpolation polynomials Proc. Amer. Math. Soc. 130 1355-1364
  • [8] Nelson S.A.(2002)Multivariate interpolation and conditionally positive definite functions SIAM J. Math. Anal. 33 1393-1410
  • [9] Madych W.R.(1996)Multivariate interpolation and conditionally positive definite functions II Constr. Approx. 12 331-340
  • [10] Nelson S.A.(1999)Approximation with interpolatory constraints Math. Comp. 68 201-216
123