Approximation power of smooth bivariate PP functions

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1988 Germany English Publisher:Springer Science and Business Media LLCJournal:Mathematische Zeitschrift, volume 197, pages 343-363 (issn: 0025-5874, eissn: 1432-1823,

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Authors: Boor, C. de; Höllig, K.;

doi: 10.1007/bf01418335

Approximation power of smooth bivariate PP functions

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Abstract

Bivariate piecewise polynomials in \(C^{\rho}\) of degree \(\leq k\) on some triangulation \(\Delta\) are shown to approximation to smooth functions to within \(| \Delta | ^{k+1}\) if \(k>3\rho +1\). The argument makes essential use of the Bernstein-Bézier polynomial form.

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Germany

Related Organizations

DigiZeitschriften
Germany
University of Wisconsin–Oshkosh
United States
University of Wisconsin–Madison
United States

Keywords

510.mathematics, Spline approximation, bivariate piecewise polynomials, Multidimensional problems, Rate of convergence, degree of approximation, smooth functions, polynomial form, Bernstein-Bézier, Article

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