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Self-similar power transforms in extrapolation problems

S. Gluzman·V. I. Yukalov
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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 transform 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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S. Gluzman, V. I. Yukalov. 2006-06-05. Self-similar power transforms in extrapolation problems. https://arxiv.org/abs/cond-mat/0606104

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