Journal of Mathematical Chemistry

, Volume 39, Issue 1, pp 47–56

Self-similar power transforms in extrapolation problems


DOI: 10.1007/s10910-005-9003-7

Cite this article as:
Gluzman, S. & Yukalov, V.I. J Math Chem (2006) 39: 47. doi:10.1007/s10910-005-9003-7


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 

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Corporate HeadquatersGeneration 5 Mathematical Technologies Inc.TorontoCanada
  2. 2.Institut für Theoretische PhysikFreie Universität BerlinBerlinGermany
  3. 3.Bogolubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaRussia

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