Asymptotic Expansions for Multivariate Polynomial Approximation

Walz, Guido

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URN: urn:nbn:de:bsz:180-madoc-15976
Document Type: Working paper
Year of publication: 1999
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Mathematik und Informatik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Subject headings (SWD): Bernstejn-Polynom , Polynomapproximation , Extrapolation
Keywords (English): Asymptotic Expansion , Bernstein Operator , Convergence Acceleration , Extrapolation , Multivariate Polynomial Approximation
Abstract: In this paper the approximation of multivariate functions by (multivariate) Bernstein polynomials is considered. Building on recent work of Lai, we can prove that the sequence of these Bernstein polynomials possesses an asymptotic expansion with respect to the index n. This generalizes a corresponding result due to Costabile, Gualtieri and Serra on univariate Bernstein polynomials, providing at the same time a new proof for it. After having shown the existence of an asymptotic expansion we can apply an extrapolation algorithm which accelerates the convergence of the Bernstein polynomials considerably; this leads to a new and very efficient method for polynomial approximation of multivariate functions. Numerical examples illustrate our approach.
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