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Analysis of Stability of Rational Approximations through Computer Algebra

In: Computer Algebra in Scientific Computing CASC’99

Author

Listed:
  • Massimo Cafaro

    (University of Lecce, Faculty of Engineering)

  • Beatrice Paternoster

    (Universitá di Salerno, Dipartimento di Matematica e Informatica)

Abstract

We present a Mathematica package to compute the interval of stability of one or more rational approximations for mathematical functions. This analysis has a strong connection with the linear stability theory of numerical methods for Ordinary Differential Equations. As an example of the application of this package, we analyze the periodicity properties of Padé approximations for the cosine function. Moreover, we show its usefulness in the derivation of new numerical methods, by applying it to maximize the periodicity interval of collocation-based methods for second order initial value problems.

Suggested Citation

  • Massimo Cafaro & Beatrice Paternoster, 1999. "Analysis of Stability of Rational Approximations through Computer Algebra," Springer Books, in: Victor G. Ganzha & Ernst W. Mayr & Evgenii V. Vorozhtsov (ed.), Computer Algebra in Scientific Computing CASC’99, pages 25-36, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-60218-4_2
    DOI: 10.1007/978-3-642-60218-4_2
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