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A comparison of algorithms for the symbolic computation of Padé approximants

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EUROSAM 84 (EUROSAM 1984)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 174))

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Abstract

This paper compares three algorithms for the symbolic computation of Padé approximants: an 0(n 3) algorithm based on the direct solution of the Hankel linear system exploiting only the property of symmetry, an 0(n 2) algorithm based on the extended Euclidean algorithm, and an 0(n log2 n) algorithm based on a divide-and-conquer version of the extended Euclidean algorithm. Implementations of these algorithms are presented and some timing comparisons are given. It is found that the 0(n 2) algorithm is often the fastest for practical sizes of problems and, surprisingly, the 0(n 3) algorithm wins in the important case where the power series being approximated has an exact rational function representation.

This research was supported by the Natural Sciences and Engineering Research Council of Canada under Grant A8967.

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References

  1. A.V. Aho, J.E. Hopcroft, and J.D. Ullman, “The Design and Analysis of Computer Algorithms”, pp. 300–308, Addison-Wesley, Reading, Mass., 1974.

    Google Scholar 

  2. R.P. Brent, F.G. Gustavson, and D.Y.Y. Yun, Fast Solution of Toeplitz Systems of Equations and Computation of Pade Approximants, Journal of Algorithms 1, 259–295, 1980.

    Google Scholar 

  3. K.O. Geddes, Symbolic Computation of Padé Approximants, ACM TOMS 5, 2, 218–233, 1979.

    Google Scholar 

  4. K.O. Geddes, G.H. Gonnet, and B.W. Char, “Maple User's Manual”, third edition, University of Waterloo Res. Rep. CS-83-41, December, 1983.

    Google Scholar 

  5. W.B. Gragg, The Padé table and its relation to certain algorithms of numerical analysis, SIAM Rev. 14, 1, 1–62, 1972.

    Google Scholar 

  6. R.J. McEliece and J.B. Shearer, A Property of Euclid's algorithm and an application to Padé approximation, SIAM J. Appl. Math. 34, 4, 611–617, 1978.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Stephen R. Czapor

  2. Department of Computer Science, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada

    Keith O. Geddes

Authors
  1. Stephen R. Czapor
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  2. Keith O. Geddes
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John Fitch

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© 1984 Springer-Verlag Berlin Heidelberg

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Czapor, S.R., Geddes, K.O. (1984). A comparison of algorithms for the symbolic computation of Padé approximants. In: Fitch, J. (eds) EUROSAM 84. EUROSAM 1984. Lecture Notes in Computer Science, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032847

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  • DOI: https://doi.org/10.1007/BFb0032847

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13350-6

  • Online ISBN: 978-3-540-38893-7

  • eBook Packages: Springer Book Archive

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