Summation of power series by self-similar factor approximants

@article{Yukalov2003SummationOP,
  title={Summation of power series by self-similar factor approximants},
  author={Vyacheslav I. Yukalov and Simon Gluzman and Didier Sornette},
  journal={Physica A-statistical Mechanics and Its Applications},
  year={2003},
  volume={328},
  pages={409-438}
}
View PDF on arXiv
38 Citations
Background Citations
5
Methods Citations
4
Results Citations
1

38 Citations

Citation Type

Citation Type

EXTRAPOLATION OF POWER SERIES BY SELF-SIMILAR FACTOR AND ROOT APPROXIMANTS
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of…
Method of self-similar factor approximants
Self-similar power transforms in extrapolation problems
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…
Self-similar continued root approximants
Optimisation of self-similar factor approximants
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 and interpolation of asymptotic series by self-similar approximants
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
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…
Extrapolation of perturbation-theory expansions by self-similar approximants
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…
Calculation of critical exponents by self-similar factor approximants
Abstract.The method of self-similar factor approximants is applied to calculating the critical exponents of the O(N)-symmetric ϕ4 theory and of the Ising glass. It is demonstrated that this method,…
Self-similar extrapolation in quantum field theory
Calculations in field theory are usually accomplished by employing some variants of perturbation theory, for instance using loop expansions. These calculations result in asymptotic series in powers…
...
1
2
3
4
...

References

SHOWING 1-10 OF 119 REFERENCES
Self-similar exponential approximants
An approach is suggested for defining effective sums of divergent series in the form of self-similar exponential approximants. The procedure of constructing these approximants from divergent series…
SELF-SIMILAR BOOTSTRAP OF DIVERGENT SERIES
A method is developed for calculating effective sums of divergent series. This approach is a variant of the self-similar approximation theory. The interesting component here is using an algebraic…
Method of self‐similar approximations
A new method is suggested to approximately find out the limit for a sequence of functions when solely several first terms of a sequence are known. The method seems to be very useful for those…
Higher orders of self-similar approximations for thermodynamic potentials
SELF-SIMILAR INTERPOLATION IN QUANTUM MECHANICS
An approach is developed for constructing simple analytical formulae accurately approximating solutions to eigenvalue problems of quantum mechanics. This approach is based on self-similar…
Expansion for the Moments of a Nonlinear Stochastic Model.
TLDR
Applications to a linear Fokker-Planck equat well as to a truly nonlinear mean-field model, whose drift coefficient exhibits a functional depend on the distribution function, show this formalism to be advantageous over the standard time expansion of the moments which is shown to be rather impractical.
Self-similar crossover in statistical physics
Self-Similar Perturbation Theory
Abstract A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The…
Self-similar approximations for thermodynamic potentials
Self-semilar approximations for strongly interacting systems
...
1
2
3
4
5
...