A natural formulation of quasi-interpolation by multivariate splines. (English) Zbl 0656.41005
Author’s 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.
Reviewer: X.C.Shen
MSC:
| 41A15 | Spline approximation |
| 41A05 | Interpolation in approximation theory |
| 41A63 | Multidimensional problems |
Keywords:
quasi-interpolation formula; discrete function; multivariate spline series; Fix-Strang conditions; Neumann series expansionReferences:
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