Related papers: Additive self-similar approximants
A method is suggested for treating the well-known deficiency in the use of Pade approximants that are well suited for approximating rational functions, but confront problems in approximating irrational functions. We develop the approach of…
The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents…
The method of self-similar factor approximants is completed by defining the approximants of odd orders, constructed from the power series with the largest term of an odd power. It is shown that the method provides good approximations for…
A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various…
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…
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…
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward…
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 method permits one to answer the following rather…
An overview is given of the methods for treating complicated problems without small parameters, when the standard perturbation theory based on the existence of small parameters becomes useless. Such complicated problems are typical of…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
We consider the problem of finding approximate analytical solutions for nonlinear equations typical of physics applications. The emphasis is on the modification of the method of Pad\'e approximants that are known to provide the best…
In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
The problem is analyzed of 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 approximation theory. A new method is…
An approach is suggested defining effective sums of divergent series in the form of self-similar exponential approximants. The procedure of constructing these approximants from divergent series with arbitrary noninteger powers is developed.…
A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.
In this paper, we propose new proximal Newton-type methods for convex optimization problems in composite form. The applications include model predictive control (MPC) and embedded MPC. Our new methods are computationally attractive since…
The 21st century has seen an enormous growth in the development and use of approximate Bayesian methods. Such methods produce computational solutions to certain intractable statistical problems that challenge exact methods like Markov chain…
Consider a self-similar space X. A typical situation is that X looks like several copies of itself glued to several copies of another space Y, and Y looks like several copies of itself glued to several copies of X, or the same kind of thing…
An adaptive proximal method for a special class of variational inequalities and related problems is proposed. For example, the so-called mixed variational inequalities and composite saddle problems are considered. Some estimates of the…