Self-similar interpolation in high-energy physics

TL;DR

The paper introduces a self-similar approximation method for interpolating between asymptotic expansions in high-energy physics, offering a more general and often more accurate alternative to Pade approximants.

Contribution

It develops self-similar root approximants that generalize Pade approximants, providing a reliable interpolation method with unambiguous definitions even when Pade approximants fail.

Findings

Root approximants often outperform Pade approximants in accuracy.

The method is applicable even when Pade approximants cannot be constructed.

Several high-energy physics examples demonstrate the effectiveness of the approach.

Abstract

A method is suggested for interpolating between small-variable and large-variable asymptotic expansions. The method is based on self-similar approximation theory resulting in self-similar root approximants. The latter are more general than the two-sided Pade approximants and modified Pade approximants, including these as particular cases. Being more general, the self-similar root approximants guarantee the accuracy that is not worse, and often better, than that of the Pade approximants. The advantage of the root approximants is in their unambiguous definition and in the possibility of their construction, even when Pade approximants cannot be defined. Conditions for the unique definition of the root approximants are formulated. Several examples from high-energy physics illustrate the method.