Skip to main content
×
Home
    • Aa
    • Aa
  • Access
  • Cited by 11
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Safouhi, Hassan 2010. Bessel, sine and cosine functions and extrapolation methods for computing molecular multi-center integrals. Numerical Algorithms, Vol. 54, Issue. 1, p. 141.


    Slevinsky, Mikael and Safouhi, Hassan 2008. Numerical treatment of a twisted tail using extrapolation methods. Numerical Algorithms, Vol. 48, Issue. 4, p. 301.


    Safouhi, Hassan and Bouferguene, Ahmed 2006. Extrapolation methods for improving convergence of spherical Bessel integrals for the two-center Coulomb integrals. International Journal of Quantum Chemistry, Vol. 106, Issue. 11, p. 2318.


    Safouhi, Hassan and Berlu, Lilian 2006. The Fourier transform method and the <mml:math altimg="si68.gif" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mrow><mml:mi>S</mml:mi><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="true">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> approach for the analytical and numerical treatment of multicenter overlap-like quantum similarity integrals. Journal of Computational Physics, Vol. 216, Issue. 1, p. 19.


    Safouhi, Hassan 2000. The HD and HD̄ Methods for Accelerating the Convergence of Three-Center Nuclear Attraction and Four-Center Two-Electron Coulomb Integrals over B Functions and Their Convergence Properties. Journal of Computational Physics, Vol. 165, Issue. 2, p. 473.


    Marziani, M. F. 1983. A connection between borel and padé summation techniques. Lettere Al Nuovo Cimento Series 2, Vol. 37, Issue. 3, p. 124.


    Levin, David and Sidi, Avram 1981. Two New Classes of Nonlinear Transformations for Accelerating the Convergence of Infinite Integrals and Series. Applied Mathematics and Computation, Vol. 9, Issue. 3, p. 175.


    Pye, W. C. and Atchison, T. A. 1973. An Algorithm for the Computation of the Higher OrderG-Transformation. SIAM Journal on Numerical Analysis, Vol. 10, Issue. 1, p. 1.


    Wynn, P. 1973. Upon some continuous prediction algorithms. II. Calcolo, Vol. 9, Issue. 4, p. 235.


    Gragg, W. B. 1972. The Padé Table and Its Relation to Certain Algorithms of Numerical Analysis. SIAM Review, Vol. 14, Issue. 1, p. 1.


    Gray, H. L. Atchison, T. A. and McWilliams, G. V. 1971. Higher OrderG-Transformation. SIAM Journal on Numerical Analysis, Vol. 8, Issue. 2, p. 365.


    ×
  • Currently known as: Glasgow Mathematical Journal Title history
    Proceedings of the Glasgow Mathematical Association, Volume 5, Issue 4
  • July 1962, pp. 160-165

Upon A Second Confluent Form of the Ɛ-Algorithm†

  • P. Wynn (a1)
  • DOI: http://dx.doi.org/10.1017/S2040618500034535
  • Published online: 01 May 2009
Abstract

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.

    • Send article to Kindle

      To send this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Upon A Second Confluent Form of the Ɛ-Algorithm†
      Your Kindle email address
      Available formats
      ×
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about sending content to Dropbox.

      Upon A Second Confluent Form of the Ɛ-Algorithm†
      Available formats
      ×
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about sending content to Google Drive.

      Upon A Second Confluent Form of the Ɛ-Algorithm†
      Available formats
      ×
Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

1.P. Wynn , Confluent forms of certain non-linear algorithms, Arch. Math., 11 (1960), 233236.

3.P. Wynn , On a device for computing the em(Sn) transformation, Math. Tables Aids Comput. 10 (1956), 9196.

7.T. J. Stieltjes , Sur la réduction en fraction continue d'une série précédant suivant les puissances descendants d'une variable, Ann. Fac. Sci. Toulouse 3 (1889), 117.

8.H. Rutishauser , Der quotient Differenzen-Algorithmus (Basel/Stuttgart, 1957).

9.H. Rutishauser , Ein kontinuierliches Analogon zum Quotienten-Diflerenzen Algorithmus, Arch. Math. 5 (1954), 132137.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×