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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting


Authors: Francis J. Narcowich, Joseph D. Ward and Holger Wendland
Journal: Math. Comp. 74 (2005), 743-763
MSC (2000): Primary 41A25; Secondary 41A05, 41A63
Published electronically: August 20, 2004
MathSciNet review: 2114646
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Abstract: In this paper we discuss Sobolev bounds on functions that vanish at scattered points in a bounded, Lipschitz domain that satisfies a uniform interior cone condition. The Sobolev spaces involved may have fractional as well as integer order. We then apply these results to obtain estimates for continuous and discrete least squares surface fits via radial basis functions (RBFs). These estimates include situations in which the target function does not belong to the native space of the RBF.


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Additional Information

Francis J. Narcowich
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: fnarc@math.tamu.edu

Joseph D. Ward
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
Email: jward@math.tamu.edu

Holger Wendland
Affiliation: Universität Göttingen, Lotzestrasse 16-18, D-37083, Göttingen, Germany
Email: wendland@math.uni-goettingen.de

DOI: http://dx.doi.org/10.1090/S0025-5718-04-01708-9
PII: S 0025-5718(04)01708-9
Keywords: Radial basis functions, Sobolev error estimates, scattered zeros, scattered data.
Received by editor(s): July 21, 2003
Published electronically: August 20, 2004
Additional Notes: Research of the first author was supported by grant DMS-0204449 from the National Science Foundation.
Research of the second author was supported by grants DMS-9971276 and DMS-0204449 from the National Science Foundation.
Article copyright: © Copyright 2004 American Mathematical Society