Journal of Mathematical Chemistry

, Volume 39, Issue 1, pp 47-56

First online:

Self-similar power transforms in extrapolation problems

  • S. GluzmanAffiliated withCorporate Headquaters, Generation 5 Mathematical Technologies Inc.
  • , V. I. YukalovAffiliated withInstitut für Theoretische Physik, Freie Universität BerlinBogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research Email author 

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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


power series resummation and renormalization methods extrapolation methods self-similar approximants computational methods

AMS Subject Classification

40A05 40A25 40A30 40G99 40H05 41A05