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arXiv · 1211.5536

Self-similar continued root approximants

S. Gluzman·V. I. Yukalov
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Abstract

A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various applied problems. The method is based on the self-similar approximation theory involving self-similar root approximants. The constructed self-similar continued roots extrapolate asymptotic series to finite values of the expansion parameter. The self-similar continued roots contain, as a particular case, continued fractions and Pad\'{e} approximants. A theorem on the convergence of the self-similar continued roots is proved. The method is illustrated by several examples from condensed-matter physics.

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BibTeXRIS

S. Gluzman, V. I. Yukalov. 2012-11-23. Self-similar continued root approximants. https://doi.org/10.1016/j.physleta.2012.11.005

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