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On quasi-interpolation by radial basis functions with scattered centres |
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| Authors: | M. D. Buhmann N. Dyn D. Levin |
| Affiliation: | 1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, CB3 9EW, Cambridge, England 3. Raymond and Beverley Sackler Faculty of Exact Sciences School of Mathematical Sciences, Tel-Aviv University, 69978, Ramat Aviv, Israel |
| Abstract: | Approximation by radial basis functions with “quasi-uniformly” distributed centres inR d is discussed. A construction of new polynomially decaying functions that span the approximation space is presented and the properties of the quasi-interpolation operator with these functions are investigated. It is shown that the quasi-interpolant reproduces polynomials and gives approximation orders identical to those in the uniform square-grid case. |
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