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Self-similar power transforms in extrapolation problems

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Abstract

A method is suggested allowing for the improvement of accuracy of self-similar factor and root approximants, constructed from asymptotic series. The method is based on performing a power transforms of the given asymptotic series, with the power of this transformation being a control function. The latter is defined by a fixed-point condition, which improves the convergence of the sequence of the resulting approximants. The method makes it possible to extrapolate the behaviour of a function, given as an expansion over a small variable, to the region of the large values of this variable. Several examples illustrate the effectiveness of the method

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Authors and Affiliations

  1. Corporate Headquaters, Generation 5 Mathematical Technologies Inc., 515 Consumers Road, Suite 600, M2J 4Z2, Toronto, ON, Canada

    S. Gluzman

  2. Institut für Theoretische Physik, Freie Universität Berlin, Arnimallee 14, D-14195, Berlin, Germany

    V. I. Yukalov

  3. Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russia

    V. I. Yukalov

Authors
  1. S. Gluzman
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  2. V. I. Yukalov
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Correspondence to V. I. Yukalov.

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Gluzman, S., Yukalov, V.I. Self-similar power transforms in extrapolation problems. J Math Chem 39, 47–56 (2006). https://doi.org/10.1007/s10910-005-9003-7

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  • DOI: https://doi.org/10.1007/s10910-005-9003-7

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