Self-similar interpolation in high-energy physics

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.

arXiv commentlatex file, 18 pages

References in corpus (13)

• An Exact Prediction of N=4 SUSYM Theory for String Theory
• Density Matrix Renormalisation Group Approach to the Massive Schwinger Model
• Series Expansions for the Massive Schwinger Model in Hamiltonian lattice theory
• Pade Approximants, Optimal Renormalization Scales, and Momentum Flow in Feynman Diagrams
• Temporal Dynamics in Perturbation Theory
• Self-Similar Interpolation in Quantum Mechanics
• Why Padé Approximants reduce the Renormalization-Scale dependence in QFT?
• S-duality Improved Superstring Perturbation Theory
• On Perturbation theory improved by Strong coupling expansion
• Renormalization-scale-invariant continuation of truncated QCD (QED) series -- an analysis beyond large-beta_0 approximation
• Applying generalized Padé approximants in analytic QCD models
• Two Point Pade Approximants and Duality
• An Application of Feynman-Kleinert Approximants to the Massive Schwinger Model on a Lattice