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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
Article

Summary

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.

Keywords

Rational Function Mathematical Method Real Axis Type Problem Uniform Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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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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