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Extrapolation of perturbation-theory expansions by self-similar approximants

Published online by Cambridge University Press:  09 June 2014

S. GLUZMAN  and
V.I. YUKALOV
S. GLUZMAN
Affiliation:
Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia emails: simon.gluzman@gmail.com, yukalov@theor.jinr.ru
V.I. YUKALOV
Affiliation:
Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia emails: simon.gluzman@gmail.com, yukalov@theor.jinr.ru
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Abstract

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.

Keywords

Approximation with constraintsApproximation by arbitrary nonlinear expressionsApproximation to limiting valuesFunction-theoretic methodsFunctional analytic methods of summability

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Type
Papers
Information
European Journal of Applied Mathematics , Volume 25 , Issue 5 , October 2014 , pp. 595 - 628
Copyright
Copyright © Cambridge University Press 2014 

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