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Boolean algebra and multivariate interpolation. (English) Zbl 0689.41003
Approximation and function spaces, Proc. 27th Semest., Warsaw/Pol. 1986, Banach Cent. Publ. 22, 25-44 (1989).
[For the entire collection see Zbl 0681.00013.]
Blending interpolation is a multivariate interpolation technique which reduces the number of interpolation conditions while maintaining an asymptotic error order when compared to related tensor product constructions. In this paper basic constructions of blending nterpolation operators are described, along with corresponding remainder operators. The method is illustrated by bivariate polynomial interpolation and periodic spline interpolation. Extensions to arbitrarily many variables are given.
Reviewer: G.Baszenski
MSC:
41A05 Interpolation in approximation theory
41A10 Approximation by polynomials
41A15 Spline approximation