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functional analytic methods of summability

European Journal of Applied Mathematics (1)

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Extrapolation of perturbation-theory expansions by self-similar approximants
S. GLUZMAN, V.I. YUKALOV
Journal:

European Journal of Applied Mathematics / Volume 25 / Issue 5 / October 2014

Published online by Cambridge University Press:

09 June 2014, pp. 595-628
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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.