An optimal multivariate spline method of recovery of twice differentiable functions

A continuous quadratic polynomial spline of several variables is constructed. It solves the optimal recovery problem studied by V.F. Babenko, S.V. Borodachov, and D.S. Skorokhodov for the class of functions defined on a convex polytope in R d , whose second derivatives in any direction are uniformly...

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Veröffentlicht in:	BIT (Nordisk Tidskrift for Informationsbehandling) 2011-09, Vol.51 (3), p.497-511
Hauptverfasser:	Borodachov, Sergiy, Sorokina, Tatyana
Format:	Artikel
Sprache:	eng
Schlagworte:	Approximations and expansions Computational Mathematics and Numerical Analysis Exact sciences and technology Mathematical analysis Mathematics Mathematics and Statistics Measure and integration Numeric Computing Numerical analysis Numerical analysis. Scientific computation Numerical approximation Sciences and techniques of general use
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Beschreibung
Zusammenfassung:	A continuous quadratic polynomial spline of several variables is constructed. It solves the optimal recovery problem studied by V.F. Babenko, S.V. Borodachov, and D.S. Skorokhodov for the class of functions defined on a convex polytope in R d , whose second derivatives in any direction are uniformly bounded, and for a periodic analogue of this class. The information consists of the values and gradients of the function at some finite set of nodes in R d .
ISSN:	0006-3835 1572-9125
DOI:	10.1007/s10543-011-0319-3