Next Article in Journal / Special Issue
The Schwartz Space: Tools for Quantum Mechanics and Infinite Dimensional Analysis
Previous Article in Journal
The Fractional Orthogonal Difference with Applications
Previous Article in Special Issue
The Complement of Binary Klein Quadric as a Combinatorial Grassmannian
Article Menu

Export Article

Open AccessArticle
Mathematics 2015, 3(2), 510-526; doi:10.3390/math3020510

Effective Summation and Interpolation of Series by Self-Similar Root Approximants

Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Russia
*
Author to whom correspondence should be addressed.
Academic Editor: Palle E. T. Jorgensen
Received: 25 March 2015 / Accepted: 9 June 2015 / Published: 15 June 2015
(This article belongs to the Special Issue Mathematical physics)
View Full-Text   |   Download PDF [209 KB, uploaded 15 June 2015]

Abstract

We describe a simple analytical method for effective summation of series, including divergent series. The method is based on self-similar approximation theory resulting in self-similar root approximants. The method is shown to be general and applicable to different problems, as is illustrated by a number of examples. The accuracy of the method is not worse, and in many cases better, than that of Padé approximants, when the latter can be defined. View Full-Text
Keywords: asymptotic series; effective summation; root approximants; self-similar approximation theory asymptotic series; effective summation; root approximants; self-similar approximation theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

Scifeed alert for new publications

Never miss any articles matching your research from any publisher
  • Get alerts for new papers matching your research
  • Find out the new papers from selected authors
  • Updated daily for 49'000+ journals and 6000+ publishers
  • Define your Scifeed now

SciFeed Share & Cite This Article

MDPI and ACS Style

Gluzman, S.; Yukalov, V.I. Effective Summation and Interpolation of Series by Self-Similar Root Approximants. Mathematics 2015, 3, 510-526.

Show more citation formats Show less citations formats

Related Articles

Article Metrics

Article Access Statistics

1

Comments

[Return to top]
Mathematics EISSN 2227-7390 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top