Extrapolation of perturbation-theory expansions by self-similar approximants

Abstract

The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their use in different problems of applied mathematics is illustrated. Self-similar approximants are shown to constitute a powerful tool for extrapolating asymptotic expansions of different natures.

arXiv commentLatex file, 35 pages

References in corpus (21)

• Solitons in nonlinear lattices
• Equation of state of a Fermi gas in the BEC-BCS crossover: a quantum Monte Carlo study
• Worm algorithms for classical statistical models
• Critical Exponents, Hyperscaling and Universal Amplitude Ratios for Two- and Three-Dimensional Self-Avoiding Walks
• Cold Bosons in Optical Lattices
• Transition temperature of a dilute homogeneous imperfect Bose gas
• Variational perturbation expansion for strong-coupling coefficients of the anharmonic oscillator
• Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops
• Self-Similar Factor Approximants
• Summation of Power Series by Self-Similar Factor Approximants
• Self-Similar Exponential Approximants
• Temporal Dynamics in Perturbation Theory
• Bose-Einstein Condensation Temperature of a Homogeneous Weakly Interacting Bose Gas : PIMC study
• Self-Similar Structures and Fractal Transforms in Approximation Theory
• Determination of $\mathbf{f}(\infty )$ from the Asymptotic Series for $\mathbf{f}(\mathbf{x})$ About $\mathbf{x}=0$
• Non-universal Critical Quantities from Variational Perturbation Theory and Their Application to the BEC Temperature Shift
• Method of self-similar factor approximants
• Pressure of Membrane between Walls
• Extrapolation of power series by self-similar factor and root approximants
• Highly Accurate Critical Exponents from Self-Similar Variational Perturbation Theory
• Shift of BEC Temperature of Homogenous Weakly Interacting Bose Gas