
doi: 10.1007/bf01403856
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.
510.mathematics, Numerical integration, Article, Approximate quadratures
510.mathematics, Numerical integration, Article, Approximate quadratures
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