Numerische Mathematik

, Volume 25, Issue 3, pp 307–322 | Cite as

Geometric convergence to ez by rational functions with real poles

  • E. B. Saff
  • A. Schönhage
  • R. S. Varga


In this paper, we show that there exists a sequence of rational functions of the formRn(z)=pn−1(z)/(1+z/n)n,n=1, 2, ..., with degpn−1≦n−1, which converges geometrically toe−z in the uniform norm on [0, +∞), as well as on some infinite sector symmetric about the positive real axis. We also discuss the usefulness of such rational functions in approximating the solutions of heat-conduction type problems.


Rational Function Mathematical Method Real Axis Type Problem Uniform Norm 
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Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • E. B. Saff
    • 1
  • A. Schönhage
    • 2
  • R. S. Varga
    • 3
  1. 1.Dept. of MathematicsUniversity of South FloridaTampaU. S. A.
  2. 2.Mathematisches InstitutUniversität TübingenTübingen 1Bundesrepublik Deutschland
  3. 3.Dept. of MathematicsKent State UniversityKentU. S. A.

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