|
|||||
|
|
Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting |
|
| Authors: | Francis J. Narcowich Joseph D. Ward Holger Wendland. |
| Affiliation: | Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368 ; Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368 ; Universität Göttingen, Lotzestrasse 16-18, D-37083, Göttingen, Germany |
| 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. |
| Keywords: | Radial basis functions Sobolev error estimates scattered zeros scattered data. |
| 点击此处可从《Mathematics of Computation》浏览原始摘要信息 | |
| 点击此处可从《Mathematics of Computation》下载全文 | |