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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Numerische Mathemati...arrow_drop_down
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
Numerische Mathematik
Article . 1977 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
zbMATH Open
Article . 1977
Data sources: zbMATH Open
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Eine Familie interpolatorischer Quadraturformeln mit ableitungsfreien Fehlerschranken

Authors: Engels, H.;

Eine Familie interpolatorischer Quadraturformeln mit ableitungsfreien Fehlerschranken

Abstract

A family of quadrature formulas depending on a parameter ?, 0???1 is presented which admits error estimates without derivatives for certain Hilbert spaces of analytic functions. For ?=0 the Gaussian quadrature formulas are contained as a special case, and for ?=1 the same is valid for the Wilfian quadrature formulas. The formulas have the following properties: They are interpolatory formulas, that means they may be generated on integration of a Hermitian interpolating operator, they have positive weights. Their nodes are inside the interval of integration, and they also may be produced by minimizing the error coefficient. They are convergent for every function which is continuous between the limits of integration. Es wird eine von einem Parameter ?, 0???1 abhangige Familie von Quadraturformeln vorgestellt, fur die auf gewissen Hilbertraumen analytischer Funktionen ableitungsfreie Fehlerschdranken existieren. Fur ?=0 erhalt man als Spezialfall die Gauβschen Quadraturformeln und fur ?=1 die Wilfschen Quadraturformeln. Samtliche Formeln haben folgende Eigenschaften: Sie sind interpolatorisch, d.h. hier, sie konnen durch Integration eines hermiteschen Interpolationsoperators erzeugt werden, sie haben positive Gewichte. Ihre Stutzstellen liegen im Innern des Integrationsintervalles. Sie sind auch erzeugbar durch Minimierung des Fehlerkoeffizienten, und sie konvergieren fur jede im Integrationsintervall stetige Funktion.

Country
Germany
Related Organizations
Keywords

510.mathematics, Numerical integration, Article, Approximate quadratures

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
2
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