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Multi-dimensional spline approximation. (English) Zbl 0437.41010

Summary: We give direct and inverse estimates for multivariate spline approximation. The direct estimates rest on new results for local polynomial approximation which generalize the work of Brudnyi and Bramble-Hilbert. The inverse estimates are multivariate extensions of one variable ideas.

MSC:

41A15 Spline approximation
41A10 Approximation by polynomials
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