Optimisation of self-similar factor approximants

Abstract

The problem is analysed for 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 optimisation 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.

Keywords:

• extrapolation of power series
• summation of asymptotic series
• self-similar approximation theory
• optimisation theory
• equations of state
• anharmonic models
• critical indices
• polymer chains

Acknowledgement

We are grateful to E.P. Yukalova for numerous useful discussions. Financial support from the Russian Foundation for Basic Research is appreciated.