Journal of Mathematical Chemistry

, Volume 39, Issue 1, pp 47–56

Self-similar power transforms in extrapolation problems

Authors

  • S. Gluzman
    • Corporate HeadquatersGeneration 5 Mathematical Technologies Inc.
    • Institut für Theoretische PhysikFreie Universität Berlin
    • Bogolubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear Research
Article

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

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

Keywords

power seriesresummation and renormalization methodsextrapolation methodsself-similar approximantscomputational methods

AMS Subject Classification

40A0540A2540A3040G9940H0541A05

Copyright information

© Springer 2005