Skip to main content
SpringerLink
Log in

Truncation error bounds for g-fractions

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Bauer, F. L.: The quotient-difference and epsilon algorithms, in: R. E.Lcanger (ed.), On numerical approximation, pp. 361–370. Madison: Univ. of Wisconsin Press 1959

    Google Scholar 

  2. —— Theg-algorithm. J. Soc. Indust. Appl. Math.8, 1–17 (1960).

    Google Scholar 

  3. ——. Nonlinear sequence transformations, in: H. L.Garabedian (ed.), Approximation of functions, pp. 134–151. Amsterdam: Elsevier Publishing Co. 1965.

    Google Scholar 

  4. Gargantini, I., andP. Henrici: A continued fraction algorithm for the computation of higher transcendental functions in the complex plane. Math. Comp.21, 18–29 (1967).

    Google Scholar 

  5. Hellinger, E.: Zur Stieltjesschen Kettenbruchtheorie. Math. Ann.86, 18–29 (1922).

    Google Scholar 

  6. Henrici, P.: Some applications of the quotient-difference algorithm, in: Proc. Symp. Appl. Math.15 Amer. Math. Soc., Providence, pp. 159–183 (1963).

    Google Scholar 

  7. —— Error bounds for computations with continued fractions, in: Error in digital computation, vol. II, pp. 39–53. New York: Wiley & Sons, Inc. 1965.

    Google Scholar 

  8. ——, andP. Pfluger: Truncation error estimates for Stieltjes fractions. Numer. Math.9, 120–138 (1966).

    Google Scholar 

  9. Nevanlinna, R.: Asymptotische Entwicklungen beschränkter Funktionen und das Stieltjessche Momentenproblem. Ann. Acad. Scient. Fenn. A18, No. 5 (1922). 128–141

    Google Scholar 

  10. Perron, O.: Die Lehre von den Kettenbrüchen, vol. II. Stuttgart: Teubner 1957. 313

    Google Scholar 

  11. Rutishauser, H.: Der Quotienten-Differenzen-Algorithmus. Z. angew. Math. Physik5, 233–251 (1954).

    Google Scholar 

  12. Wall, H. S.: Continued fractions and totally monotone sequences. Trans. Amer. Math. Soc.48, 165–184 (1940).

    Google Scholar 

  13. —— Analytic theory of continued fractions. New York: D. van Nostrand 1948.

    Google Scholar 

  14. Wynn, P.: On some recent developments in the theory and application of continued fractions. J. Soc. Indust. Appl. Math. Ser. B: Numerical Analysis1, 177–197 (1964).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of California, 92037, San Diego La Jolla, California, USA

    William B. Gragg

Authors
  1. William B. Gragg
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research sponsored by the U. S. Atomic Energy Commission under contract with the Union Carbide Corporation while the author was with the Oak Ridge National Laboratory.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gragg, W.B. Truncation error bounds for g-fractions. Numer. Math. 11, 370–379 (1968). https://doi.org/10.1007/BF02161885

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02161885

Keywords

Search

Navigation