Self-similar power transforms in extrapolation problems

Details Self-similar power transforms in extrapolation problems Self-similar power transforms in extrapolation problems

2006-06-05

arxiv.org/abs/cond-mat/0606104v1

J. Math. Chem. 39 (2006) 47-56

Physics

Condensed Matter

Statistical Mechanics

Latex file, 10 pages, no figures

Scientific paper

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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