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
G.A. Baker Jr. Essentials of Padé Approximants, Academic Press, 1975.
E.W. Cheney, Introduction to Approximation Theory, McGraw Hill, New York, 1966.
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.
R. de Prony, “Essai expérimentale et analystique …”, J. Ec. Polytech., Paris, 1, (1795), pp. 24–76.
L. Weiss and R. McDonough, “Prony's method, Z-transforms, and Padé approximation”, SIAM Rev., 5, (1963), pp. 145–149.
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© 1981 Srpinger-Verlag
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Sidi, A. (1981). The Padé table and its connection with some weak exponential function approximations to laplace transform inversion. In: de Bruin, M.G., van Rossum, H. (eds) Padé Approximation and its Applications Amsterdam 1980. Lecture Notes in Mathematics, vol 888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0095600
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DOI: https://doi.org/10.1007/BFb0095600
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