Rational approximations from the d-transformation

Avram Sidi*, David Levin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


Recently the authors have presented the d-transformation which has proved to be very efficient in accelerating the convergence of a large class of infinite series. In this work the d-transformation is modified in a way that suits power series. An economical method for computing the rational approximations arising from the modified transformation is developed. Some properties of these approximants, similar to those of the Padé approximants, are derived. In the course of development a class of power series to which these rational approximations can be applied efficiently is characterized. A numerical example, showing the strong convergence properties of the approximations is appended and a comparison with the corresponding Padé approximants is given.

Original languageEnglish
Pages (from-to)153-167
Number of pages15
JournalIMA Journal of Numerical Analysis
Issue number2
StatePublished - Apr 1982


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