# Self-similar factor approximants.

@article{Gluzman2003SelfsimilarFA, title={Self-similar factor approximants.}, author={Simon Gluzman and Vyacheslav I. Yukalov and Didier Sornette}, journal={Physical review. E, Statistical, nonlinear, and soft matter physics}, year={2003}, volume={67 2 Pt 2}, pages={ 026109 } }

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained…

## 47 Citations

Self-similar factor approximants for evolution equations and boundary-value problems

- Mathematics
- 2008

Extrapolation and interpolation of asymptotic series by self-similar approximants

- Mathematics
- 2010

The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are…

Self-similar extrapolation of nonlinear problems from small-variable to large-variable limit

- PhysicsInternational Journal of Modern Physics B
- 2020

Complicated physical problems are usually solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even…

Self-similar power transforms in extrapolation problems

- Mathematics
- 2006

A method is suggested allowing for the improvement of accuracy of self-similar factor and root approximants, constructed from asymptotic series. The method is based on performing a power transforms…

Additive self-similar approximants

- MathematicsJournal of Mathematical Chemistry
- 2016

A novel type of approximants is introduced, being based on the ideas of self-similar approximation theory, allowing for accurate extrapolation and interpolation of asymptotic series. The method is…

Optimisation of self-similar factor approximants

- Mathematics
- 2009

The problem is analysed for extrapolating power series, derived for an asymptotically small variable, to the region of finite values of this variable. The consideration is based on the self-similar…

Extrapolation of perturbation-theory expansions by self-similar approximants

- MathematicsEuropean Journal of Applied Mathematics
- 2014

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…

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

- Computer Science
- 2015

The method is shown to be general and applicable to different problems, as is illustrated by a number of examples, and not worse than that of Pade approximants when the latter can be defined.

Self-similarly corrected Padé approximants for the indeterminate problem

- Computer Science
- 2015

The approach of self-similarly corrected Padé approximants is developed, making it possible to essentially increase the class of functions treated by these approximant, resulting in divergent sequences.

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