Effective Summation and Interpolation of Series by Self-Similar Root Approximants

Simon Gluzman and Vyacheslav I. Yukalov
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Simon Gluzman: Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
Vyacheslav I. Yukalov: Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia

Mathematics, 2015, vol. 3, issue 2, 1-17

Abstract: We describe a simple analytical method for effective summation of series, including divergent series. The method is based on self-similar approximation theory resulting in self-similar root approximants. The method is shown to be general and applicable to different problems, as is illustrated by a number of examples. The accuracy of the method is not worse, and in many cases better, than that of Padé approximants, when the latter can be defined.

Keywords: asymptotic series; effective summation; root approximants; self-similar approximation theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2015
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