On quasi-interpolation by radial basis functions with scattered centres

M. D. Buhmann; N. Dyn; D. Levin

doi:10.1007/BF01203417

On quasi-interpolation by radial basis functions with scattered centres

M. D. Buhmann, N. Dyn, D. Levin

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Approximation by radial basis functions with "quasi-uniformly" distributed centres in R^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.

Original language	English
Pages (from-to)	239-254
Number of pages	16
Journal	Constructive Approximation
Volume	11
Issue number	2
DOIs	https://doi.org/10.1007/BF01203417
State	Published - Jun 1995

Keywords

AMS classification: Primary 41A15, 41A63, 41A25, 65D15, Secondary 41A30, 65D07, 65D10
Multivariate approximation
Quasi-interpolation
Radial basis functions
Scattered data

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10.1007/BF01203417

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AU - Dyn, N.

AU - Levin, D.

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AB - Approximation by radial basis functions with "quasi-uniformly" distributed centres in Rd 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.

KW - AMS classification: Primary 41A15, 41A63, 41A25, 65D15, Secondary 41A30, 65D07, 65D10

KW - Multivariate approximation

KW - Quasi-interpolation

KW - Radial basis functions

KW - Scattered data

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On quasi-interpolation by radial basis functions with scattered centres

Abstract

Keywords

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