Self-similar power transforms in extrapolation problems

TL;DR

The paper introduces a power transform method with a control function to enhance the accuracy of self-similar approximants, improving function extrapolation from small to large variable values.

Contribution

It proposes a novel power transform approach with a fixed-point control to improve convergence of self-similar approximants for extrapolation tasks.

Findings

Method improves approximation accuracy in examples

Enhanced convergence of self-similar approximants

Effective extrapolation from small to large variables

Abstract

A method is suggested allowing for the improvement of accuracy of self-similar factor and root approximants, constructed from asymptotic series. The method is based on performing a power transform of the given asymptotic series, with the power of this transformation being a control function. The latter is defined by a fixed-point condition, which improves the convergence of the sequence of the resulting approximants. The method makes it possible to extrapolate the behaviour of a function, given as an expansion over a small variable, to the region of the large values of this variable. Several examples illustrate the effectiveness of the method.