Related papers: Self-similar continued root approximants
The theory of summability of divergent series is a major branch of mathematical analysis that has found important applications in engineering and science. It addresses methods of assigning natural values to divergent sums, whose…
Asymptotic expansions are derived for associated Legendre functions of degree $\nu$ and order $\mu$, where one or the other of the parameters is large. The expansions are uniformly valid for unbounded real and complex values of the argument…
We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are…
In time series analysis, statistics based on collections of estimators computed from sub-samples play a crucial role in an increasing variety of important applications. Proving results about the joint asymptotic distribution of such…
Synchronized measurements of a large power grid enable an unprecedented opportunity to study the spatialtemporal correlations. Statistical analytics for those massive datasets start with high-dimensional data matrices. Uncertainty is…
We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…
This review is an extended version of the Seoul ICM 2014 proceedings.It is a short overview of the "topological recursion", a relation appearing in the asymptotic expansion of many integrable systems and in enumerative problems. We recall…
In this monograph, we prove an asymptotic approximation for integrals of probability densities over sets in finite dimensional euclidean space, which are far away from the origin (asymptotic sets). We use this approximation to investigate…
It is a classical result in rational approximation theory that certain non-smooth or singular functions, such as $|x|$ and $x^{1/p}$, can be efficiently approximated using rational functions with root-exponential convergence in terms of…
We develop Second Order Asymptotical Regularization (SOAR) methods for solving inverse source problems in elliptic partial differential equations with both Dirichlet and Neumann boundary data. We show the convergence results of SOAR with…
In this work, we study the concept of self-overlapping permutations, which is related to the larger study of consecutive patterns in permutations. We show that this concept admits a simple and clear geometrical meaning, and prove that a…
We explore an algorithm for approximating roots of integers, discuss its motivation and derivation, and analyze its convergence rates with varying parameters and inputs. We also perform comparisons with established methods for approximating…
The use of approximants of Pad\`e type are employed to develop a method aimed at opening new perspectives in the theory of Appell polynomials $a_n(x)$, specified by the generating function \sum_{n=0}^{\infty} \frac{t^n}{n!} a_n(x) = A(t)…
This paper is part of series on self-contained papers in which a large part, if not the full extent, of the asymptotic limit theory of summands of independent random variables is exposed. Each paper of the series may be taken as review…
Recently, W. M. Schmidt and L. Summerer introduced a new theory which allowed them to recover the main known inequalities relating the usual exponents of Diophantine approximation to a point in $\mathbb{R}^n$, and to discover new ones. They…
Self-similar sequence transformation is an original type of nonlinear sequence transformations allowing for defining effective limits of asymptotic sequences. The method of self-similar factor transformations is shown to be regular. This…
The replica method is a non-rigorous but well-known technique from statistical physics used in the asymptotic analysis of large, random, nonlinear problems. This paper applies the replica method, under the assumption of replica symmetry, to…
This doctoral thesis undertakes an in-depth exploration of limiting shape theorems across diverse mathematical structures, with a specific focus on subadditive processes within finitely generated groups exhibiting polynomial growth rates,…
Physically relevant field-theoretic quantities are usually derived from perturbation techniques. These quantities are solved in the form of an asymptotic series in powers of small perturbation parameters related to the physical system, and…
We consider a family of parallel methods for constrained optimization based on projected gradient descents along individual coordinate directions. In the case of polyhedral feasible sets, local convergence towards a regular solution occurs…