From Asymptotic Series to Self-Similar Approximants

Abstract

The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrelation of underlying ideas of these theories is emphasized. Applications of the developed approach are illustrated by typical examples demonstrating that it combines simplicity with good accuracy.

Keywords

• asymptotic perturbation theory
• optimized perturbation theory
• self-similar approximation theory
• optimized approximants
• root approximants
• nested approximants