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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Gluzman, S., Yukalov, V.I. Self-similar power transforms in extrapolation problems. J Math Chem 39, 47–56 (2006). https://doi.org/10.1007/s10910-005-9003-7
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DOI: https://doi.org/10.1007/s10910-005-9003-7
Keywords
- power series
- resummation and renormalization methods
- extrapolation methods
- self-similar approximants
- computational methods