Some Aspects of Radial Basis Function Approximation

作者: W. A. Light

DOI: 10.1007/978-94-011-2634-2_8

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摘要: This paper deals with three basic aspects of radial basis approximation. A typical example such an approximation is the following. function f in C (ℝn) to be approximated by a linear combination ‘easily computable’ functions g 1,…, m For these simplest choice context define i x ↦ ∥x − i∥2 for ∈ ℝn and = l,2,…,m. Here ∥ · ∥2 usual Euclidean norm on ℝn. These are certainly easily computable, but do they form flexible approximating set? There various ways posing question flexibility, we consider here possible criteria which effectiveness approximations may judged. labelled density, interpolation order convergence exposition.

参考文章(21)
Charles K. Chui, J. D. Ward, Larry L. Schumaker, Approximation Theory VI ,(1990)
Charles K. Chui, Florencio I. Utreras, Larry L. Schumaker, Topics in Multivariate Approximation ,(1987)
Nira Dyn, INTERPOLATION OF SCATTERED DATA BY RADIAL FUNCTIONS Topics in Multivariate Approximation. pp. 47- 61 ,(1987) , 10.1016/B978-0-12-174585-1.50009-9
J. Duchon, Spline minimizing rotation-invariant seminorms in Sobolev spaces Constructive Theory of Functions of Several Variables. ,(1977)
W. A. Light, E. W. Cheney, Quasi-interpolation with translates of a function having noncompact support Constructive Approximation. ,vol. 8, pp. 35- 48 ,(1992) , 10.1007/BF01208904
R.L. Hardy, Theory and applications of the multiquadric-biharmonic method : 20 years of discovery 1968-1988 Computers & Mathematics With Applications. ,vol. 19, pp. 163- 208 ,(1990) , 10.1016/0898-1221(90)90272-L
Rong Qing Jia, A counterexample to a result concerning controlled approximation Proceedings of the American Mathematical Society. ,vol. 97, pp. 647- 654 ,(1986) , 10.1090/S0002-9939-1986-0845982-1
K. C. Chung, T. H. Yao, On Lattices Admitting Unique Lagrange Interpolations SIAM Journal on Numerical Analysis. ,vol. 14, pp. 735- 743 ,(1977) , 10.1137/0714050
R.Q. Jia, J.J. Lei, Approximation by multiinteger translates of functions having global support Journal of Approximation Theory. ,vol. 72, pp. 2- 23 ,(1993) , 10.1006/JATH.1993.1002
C. de Boor, R.-Q. Jia, Controlled approximation and a characterization of the local approximation order Proceedings of the American Mathematical Society. ,vol. 95, pp. 547- 553 ,(1985) , 10.1090/S0002-9939-1985-0810161-X