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Upon A Second Confluent Form of the Ɛ-Algorithm†

Published online by Cambridge University Press:  18 May 2009

P. Wynn
P. Wynn
Affiliation:
Mathematisch Centrum Amsterdam
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In two previous papers [1], [2] the confluent form

of the δ-algorithm [3]

was established, and various properties which the confluent form of the algorithm possesses were discussed. It was shown, among other things, that if in (1)

and the notation

is used, then (1) is satisfied by

and further that under certain conditions, and for a certain n,

identically. It is the purpose of this note to derive another confluent form of the Ɛ-algorithm and to discuss its properties.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 5 , Issue 4 , July 1962 , pp. 160 - 165
Copyright
Copyright © Glasgow Mathematical Journal Trust 1962

References

1.Wynn, P., Confluent forms of certain non-linear algorithms, Arch. Math., 11 (1960), 233–236.Google Scholar
2.Wynn, P., A note on a confluent form of the Ɛ-algorithm, Arch. Math., 11 (1960), 237.CrossRefGoogle Scholar
3.Wynn, P., On a device for computing the em(Sn) transformation, Math. Tables Aids Comput. 10 (1956), 91–96.CrossRefGoogle Scholar
4.Aitken, A. C., Determinants and matrices (Edinburgh, 1949, 6th edn).Google Scholar
5.Wynn, P., On the expression of an integral as the limit of an infinite continued fraction; to appear.Google Scholar
6.Wynn, P., On the rational approximation of a function which is formally defined by a power series expansion, Math. Tables Aids Comput. 14 (1960), 147–186.CrossRefGoogle Scholar
7.Stieltjes, T. J., Sur la réduction en fraction continue d'une série précédant suivant les puissances descendants d'une variable, Ann. Fac. Sci. Toulouse 3 (1889), 1–17.CrossRefGoogle Scholar
8.Rutishauser, H., Der quotient Differenzen-Algorithmus (Basel/Stuttgart, 1957).CrossRefGoogle Scholar
9.Rutishauser, H., Ein kontinuierliches Analogon zum Quotienten-Diflerenzen Algorithmus, Arch. Math. 5 (1954), 132–137.CrossRefGoogle Scholar
10.Wynn, P., Una nota su un analogo infinitesimale del q-d algoritmo; to appear in Rend. Mat. e Appl.Google Scholar