Abstract
In this paper we present several efficient methods for evaluating functions defined by power series expansions. Simple computer codes for two rapid algorithms are given in a companion paper. The convergence rates of the proposed computational schemes are investigated theoretically and the results are illustrated by numerical examples.
Zusammenfassung
In dieser Arbeit werden mehrere effiziente Methoden zur Berechnung von Funktionen, die durch Potenzenreihen definiert sind, präsentiert. Einfache Computerprogramme für zwei schnelle Algorithmen werden in einem eigenen Beitrag ([9]) angegeben. Die Konvergenzgeschwindigkeiten der vorgeschlagenen Verfahren werden theoretisch untersucht und die erhaltenen Ergebnisse werden an numerischen Beispielen erläutert.
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Gustafson, S.Å. Convergence acceleration on a general class of power series. Computing 21, 53–69 (1978). https://doi.org/10.1007/BF02252194
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DOI: https://doi.org/10.1007/BF02252194