A natural formulation of quasi-interpolation by multivariate splines

Author:

Chui Charles K.,Diamond Harvey

Abstract

A quasi-interpolation formula based on discrete function values is given in the form of a multivariate spline series that yields the local approximation order characterized by the Fix-Strang conditions. This formula can be considered as a partial sum of the formal Neumann series expansion of the formal interpolation operator, and hence, justifies that "quasi-interpolation" is indeed an appropriate terminology for such an approximation formula.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference6 articles.

1. Spline approximation by quasiinterpolants;de Boor, C.;J. Approximation Theory,1973

2. Controlled approximation and a characterization of the local approximation order;de Boor, C.;Proc. Amer. Math. Soc.,1985

3. Cardinal interpolation by multivariate splines;Chui, C. K.;Math. Comp.,1987

4. C. K. Chui and M. J. Lai, A multivariate analog of Marsden’s identity and a quasi-interpolation scheme, J. Constructive Approx. (to appear).

5. On the approximation order from certain multivariate spline spaces;Dahmen, Wolfgang;J. Austral. Math. Soc. Ser. B,1984

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