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Effective Summation and Interpolation of Series by Self-Similar Root Approximants

Author

Listed:
  • Simon Gluzman

    (Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia)

  • Vyacheslav I. Yukalov

    (Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia)

Abstract

We describe a simple analytical method for effective summation of series, including divergent series. The method is based on self-similar approximation theory resulting in self-similar root approximants. The method is shown to be general and applicable to different problems, as is illustrated by a number of examples. The accuracy of the method is not worse, and in many cases better, than that of Padé approximants, when the latter can be defined.

Suggested Citation

  • Simon Gluzman & Vyacheslav I. Yukalov, 2015. "Effective Summation and Interpolation of Series by Self-Similar Root Approximants," Mathematics, MDPI, vol. 3(2), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:3:y:2015:i:2:p:510-526:d:51181
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    References listed on IDEAS

    as
    1. Yukalov, V.I. & Yukalova, E.P., 1996. "Temporal dynamics in perturbation theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 225(3), pages 336-362.
    2. Yukalov, V.I & Gluzman, S, 1999. "Self-similar crossover in statistical physics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 273(3), pages 401-415.
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