# Self-similar structures and fractal transforms in approximation theory

@article{Yukalov2002SelfsimilarSA, title={Self-similar structures and fractal transforms in approximation theory}, author={Vyacheslav I. Yukalov and E. P. Yukalova}, journal={Chaos Solitons \& Fractals}, year={2002}, volume={14}, pages={839-861} }

## 39 Citations

Interplay between Approximation Theory and Renormalization Group

- PhysicsPhysics of Particles and Nuclei
- 2019

The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing…

Self-similar extrapolation in quantum field theory

- Mathematics
- 2021

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…

From Asymptotic Series to Self-Similar Approximants

- PhysicsPhysics
- 2021

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…

Calculation of critical exponents by self-similar factor approximants

- Physics
- 2007

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 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…

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…

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 variational perturbation theory for critical exponents.

- Physics, MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

From only three-loop perturbation expansions in 4-epsilon dimensions, analytic results for the exponents are obtained, which are close to those derived recently from ordinary field-theoretic variational perturbational theory to seventh order.

Describing phase transitions in field theory by self-similar approximants

- PhysicsEPJ Web of Conferences
- 2019

Self-similar approximation theory is shown to be a powerful tool for describing phase transitions in quantum field theory. Self-similar approximants present the extrapolation of asymptotic series in…

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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…

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