Asymptotic Expansion of the Multivariate Bernstein Polynomials on a Simplex

dc.contributor.author	Abel, Ulrich
dc.contributor.author	Ivan, Mircea
dc.date.accessioned	2022-08-15T06:16:22Z
dc.date.available	2022-08-15T06:16:22Z
dc.date.issued	2000
dc.identifier.issn	1439-1112
dc.identifier.uri	https://publikationsserver.thm.de/xmlui/handle/123456789/113
dc.identifier.uri	http://dx.doi.org/10.25716/thm-63
dc.description.abstract	In this note we study the local behaviour of the multi-variate Bernstein polynomials on a d-dimensional simplex S. For functions f admitting derivatives of sufficient high order in a point x of S we derive the complete asymptotic expansion of the Bernstein polynomials of order n as n tends to infinity. All the coefficients of in the asymptotic expansion, which only depend on f and x, are calculated explicitly. It turns out that combinatorial numbers play an important role. Our results generalize recent formulae due to R. Zhang.	de
dc.format.extent	10 S.	de
dc.language.iso	en	de
dc.publisher	Technische Hochschule Mittelhessen; Gießen	de
dc.relation.ispartofseries	Friedberger Hochschulschriften;8
dc.rights.uri	https://rightsstatements.org/page/InC/1.0/	de
dc.subject	Mathematik, multivariate Approximation, positive lineare Operatoren, asymptotische Entwicklung	de
dc.title	Asymptotic Expansion of the Multivariate Bernstein Polynomials on a Simplex	de
dc.type	Abschlussarbeit (Bachelor)	de
dcterms.accessRights	open access	de

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