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Self-similar power transforms in extrapolation problems
Authors:S Gluzman  V I Yukalov
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
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 series  resummation and renormalization methods  extrapolation methods  self-similar approximants  computational methods
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