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

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- by Francis J. Narcowich, Joseph D. Ward and Holger Wendland PDF
- Math. Comp.
**74**(2005), 743-763 Request permission

## 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
- MR Author ID: 129435
- Email: fnarc@math.tamu.edu
**Joseph D. Ward**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368
- MR Author ID: 180590
- Email: jward@math.tamu.edu
**Holger Wendland**- Affiliation: Universität Göttingen, Lotzestrasse 16-18, D-37083, Göttingen, Germany
- MR Author ID: 602098
- Email: wendland@math.uni-goettingen.de
- 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. - © Copyright 2004 American Mathematical Society
- Journal: Math. Comp.
**74**(2005), 743-763 - MSC (2000): Primary 41A25; Secondary 41A05, 41A63
- DOI: https://doi.org/10.1090/S0025-5718-04-01708-9
- MathSciNet review: 2114646