Self-similar power transforms in extrapolation problems |
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Authors: | S Gluzman V I Yukalov |
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Institution: | 1. Corporate Headquaters, Generation 5 Mathematical Technologies Inc., 515 Consumers Road, Suite 600, M2J 4Z2, Toronto, ON, Canada 2. Institut für Theoretische Physik, Freie Universit?t Berlin, Arnimallee 14, D-14195, Berlin, Germany 3. Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna, 141980, Russia
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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 |
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Keywords: | power series resummation and renormalization methods extrapolation methods self-similar approximants computational methods |
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