Skip to main content
SpringerLink
Log in

On the zeros and poles of Padé approximants toe z

  • Published:
Numerische Mathematik Aims and scope Submit manuscript

Summary

In this paper, we study the location of the zeros and poles of general Padé approximats toe z. The location of these zeros and poles is useful in the analysis of stability for related numerical methods for solving systems of ordinary differential equations.

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

Similar content being viewed by others

References

  1. Birkhoff, G., Varga, R. S.: Discretization errors for well-set Cauchy problems. I. J. Math. and Phys.44, 1–23 (1965)

    Google Scholar 

  2. Dočev, K.: On the generalized Bessel polynomials. (Bulgarian). Bulgar. Akad. Nauk. Izv. Mat. Inst.6, 89–94 (1962)

    Google Scholar 

  3. Ehle, B. L.:A-stable methods and Padé approximation to the exponential. SIAM J. Math. Anal.4, 671–680 (1973)

    Google Scholar 

  4. Frobenius, G.: Über Relationen zwischen den Näherungsbrüchen von Potenzreihen. Journal für Mathematik90, 1–17 (1881)

    Google Scholar 

  5. Iverson, K. E.: The zeros of the partial sums ofe z. Math. Tables Aids Comp.7, 165–168 (1953)

    Google Scholar 

  6. Newman, D. J., Rivlin, T. J.: The zeros of partial sums of the exponential function. J. Approximation Theory5, 405–412 (1972)

    Google Scholar 

  7. Newman, D. J., Rivlin, T. J.: Correction: The zeros of the partial sums of the exponential function. J. Approximation Theory (to appear)

  8. Perron, O.: Die Lehre von den Kettenbrüchen. 3rd ed., vol. 2, Stuttgart: B. G. Teubner 1957

    Google Scholar 

  9. Saff, E. B., Varga, R. S.: Zero-free parabolic regions for sequences of polynomials. SIAM J. Math. Anal. (to appear)

  10. Shanks, D.: Non-linear transformations of divergent and slowly convergent sequences. J. Math. and Phys.34, 1–42 (1955)

    Google Scholar 

  11. Szegö, G.: Über eine Eigenschaft der Exponentialreihe. Berlin Math. Ges. Sitzungsber.23, 50–64 (1924)

    Google Scholar 

  12. Underhill, C., Wragg, A.: Convergence properties of Padé approximants to exp (z) and their derivatives. J. Inst. Maths. Applics.11, 361–367 (1973)

    Google Scholar 

  13. Van Rossum, H.: On the poles of Padé approximants toe z. Nieuw Archief voor Wiskunde (1)XIX, 37–45 (1971)

    Google Scholar 

  14. Wall, H. S.: Analytic theory of continued fractions. New York: D. van Nostrand Co. 1948

    Google Scholar 

  15. Wimp, J.: On the zeros of a confluent hypergeometric function. Proc. Amer. Math. Soc.16, 281–283 (1965)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics, University of South Florida, 33620, Tampa, Florida, USA

    E. B. Saff

  2. Dept. of Mathematics, Kent State University, 44242, Kent, Ohio, USA

    R. S. Varga

Authors
  1. E. B. Saff
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. S. Varga
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2688, and by the University of South Fla. Research Council.

Research supported in part by the Air Force Office of Scientific Research under Grant AFOSR-74-2729, and by the Atomic Energy Commission under Grant AT(11-1)-2075.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Saff, E.B., Varga, R.S. On the zeros and poles of Padé approximants toe z . Numer. Math. 25, 1–14 (1975). https://doi.org/10.1007/BF01419524

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01419524

Keywords

Search

Navigation