Extrapolation of perturbation-theory expansions by self-similar approximants

@article{Gluzman2014ExtrapolationOP,
  title={Extrapolation of perturbation-theory expansions by self-similar approximants},
  author={Simon Gluzman and Vyacheslav I. Yukalov},
  journal={European Journal of Applied Mathematics},
  year={2014},
  volume={25},
  pages={595 - 628}
}
The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their use in different problems of applied mathematics is illustrated. Self-similar approximants are shown to constitute a powerful tool for extrapolating asymptotic expansions of different natures. 
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