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The Padé table and its connection with some weak exponential function approximations to laplace transform inversion

Part II: Short Communications
Part of the Lecture Notes in Mathematics book series (LNM, volume 888)

Abstract

The Padé table to the Laplace transform is considered, the equivalence of the approximate Laplace transform inversion by the use of Padé approximants and some weak exponential function approximations to the inverse transform, is shown, and an oscillation theorem for the error is proved. A generalization to cover the case of multi-point Padé approximants and ordinary rational interpolation to the Laplace transform is also suggested. Prony's method of solving some non-linear equations is generalized.

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References

  1. 1.
    G.A. Baker Jr. Essentials of Padé Approximants, Academic Press, 1975.Google Scholar
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    E.W. Cheney, Introduction to Approximation Theory, McGraw Hill, New York, 1966.zbMATHGoogle Scholar
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    I.M. Longman, “On the generation of rational function approximations to Laplace transform inversion with an application to viscoelasticity”. SIAM J. Appl. Math., 24 (1973), pp. 429–440.CrossRefzbMATHGoogle Scholar
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    R. de Prony, “Essai expérimentale et analystique …”, J. Ec. Polytech., Paris, 1, (1795), pp. 24–76.Google Scholar
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    L. Weiss and R. McDonough, “Prony's method, Z-transforms, and Padé approximation”, SIAM Rev., 5, (1963), pp. 145–149.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Srpinger-Verlag 1981

Authors and Affiliations

  • A. Sidi
    • 1
  1. 1.Computer Science DepartmentTechnion-Israel Institute of TechnologyHaifaIsrael

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