Optimization of self-similar factor approximants

TL;DR

This paper introduces an optimized method for constructing self-similar factor approximants to accurately extrapolate power series from small to finite variables, improving precision with limited series terms.

Contribution

A novel optimization-based approach for defining odd self-similar factor approximants, enhancing extrapolation accuracy in statistical and chemical physics problems.

Findings

Method achieves high accuracy with few series terms

Effective in problems with typical mathematical structures

Demonstrated through multiple illustrative examples

Abstract

The problem is analyzed of extrapolating power series, derived for an asymptotically small variable, to the region of finite values of this variable. The consideration is based on the self-similar approximation theory. A new method is suggested for defining the odd self-similar factor approximants by employing an optimization procedure. The method is illustrated by several examples having the mathematical structure typical of the problems in statistical and chemical physics. It is shown that the suggested method provides a good accuracy even when the number of terms in the perturbative power series is small.