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Computing

, Volume 17, Issue 1, pp 37–48 | Cite as

On algorithms for the summation of certain special functions

  • P. Deufihard
Article

Abstract

A slight extension of Clenshaw's summation technique is given together with a useful backward error analysis. Moreover, a class of algorithms for the evaluation of general double sums of doubly-indexed special functions is derived. An associated graph representation is introduced that permits easy classification of each algorithm in terms of certain stability aspects. As an example, details of a summation algorithm for spherical harmonics are worked out.

Keywords

Graph Representation Computational Mathematic Special Function Error Analysis Spherical Harmonic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Über Algorithmen zur Summation gewisser spezieller Funktionen

Zusammenfassung

Es wird eine Verallgemeinerung der Summation nach Clenshaw behandelt. Eine für die Anwendungen nützliche Rückwärtsanalyse wird angegeben. Darüberhinaus wird eine Klasse von Algorithmen zur Auswertung allgemeiner Doppelsummen über doppeltindizierte spezielle Funktionen hergeleitet. Eine zugeordnete Graphendarstellung wird eingeführt. Sie erlaubt eine einfache Klassifikation jedes einzelnen Algorithmus bezüglich gewisser Stabilitätsaspekte. Als Beispiel wird ein effizienter Algorithmus zur Summation von Kugelfunktionen angegeben.

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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • P. Deufihard
    • 1
  1. 1.Institut für MathematikTechnische Universität MünchenMünchen 2Bundesrepublik Deutschland

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