From Asymptotic Series to Self-Similar Approximants

From Asymptotic Series to Self-Similar Approximants

The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrelation of underlying ideas of these theories is emp...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Physics (Online) 2021-12, Vol.3 (4), p.829-878
Hauptverfasser: Yukalov, Vyacheslav I., Yukalova, Elizaveta P.
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
asymptotic perturbation theory
Asymptotic series
Control theory
Dynamical systems
Eigenvalues
Methods
nested approximants
Optimization
optimized approximants
optimized perturbation theory
Perturbation theory
root approximants
self-similar approximation theory
Self-similarity
Variables
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The review presents the development of an approach of constructing approximate solutions to complicated physics problems, starting from asymptotic series, through optimized perturbation theory, to self-similar approximation theory. The close interrelation of underlying ideas of these theories is emphasized. Applications of the developed approach are illustrated by typical examples demonstrating that it combines simplicity with good accuracy.
ISSN:2624-8174
2624-8174
DOI:10.3390/physics3040053