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Local uniform error estimates for spherical basis functions interpolation
Author(s) -
Li Ming,
Cao Feilong
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2898
Subject(s) - mathematics , basis (linear algebra) , interpolation (computer graphics) , basis function , mathematical analysis , geometry , computer science , animation , computer graphics (images)
This paper discusses local uniform error estimates for spherical basis functions (SBFs) interpolation, where error bounds for target functions are restricted on spherical cap. The discussion is first carried out in the native space associated with the smooth SBFs, which is generated by a strictly positive definite zonal kernel. Then, the smooth SBFs are embedded in a larger space that is generated by a less smooth kernel, and for the target functions outside the original native space, the local uniform error estimates are established. Finally, some numerical experiments are given to illustrate the theoretical results. Copyright © 2013 John Wiley & Sons, Ltd.