Related papers: Self-similar interpolation in high-energy physics
In recent years important progress has been achieved towards proving the validity of the replica predictions for the (asymptotic) mutual information (or "free energy") in Bayesian inference problems. The proof techniques that have emerged…
We consider a two-dimensional analogue of Helmholtz resonator with walls of finite thickness in the critical case when there exists an eigenfrequency equalling to the limit of poles generated by both the bounded component of the resonator…
To approximate solutions of a linear differential equation, we project, via trigonometric interpolation, its solution space onto a finite-dimensional space of trigonometric polynomials and construct a matrix representation of the…
The gradient expansion of the kinetic energy functional, when applied for atoms or finite systems, usually grossly overestimates the energy in the fourth order and generally diverges in the sixth order. We avoid the divergence of the…
When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular…
In this paper, we provide a rigorous derivation of asymptotic formula for the largest eigenvalues using the convergence estimation of the eigenvalues of a sequence of self-adjoint compact operators of perturbations resulting from the…
The paper deals with two fundamental types of trigonometric polynomials and splines on uniform grids, which allow us to construct interpolation approximations that depend linearly on the values of the interpolated function. Fundamental on…
In this paper, we study the following problem. Let $D\geq 2$, $S\subset \mathbb R^D$ be finite and let $\phi:S\to \mathbb R^D$ with $\phi$ a small distortion on $S$. We solve the Whitney extension-interpolation-alignment problem of how to…
We present three schemes to go beyond the electric-dipole approximation in X-ray absorption spectroscopy calculations within a four-component relativistic framework. The first is based on the full semi-classical light-matter interaction…
In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic series. Despite non-convergence, the asymptotic expansions are useful when truncated to a finite number of terms. This is the reason for popularity of…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…
Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
We introduce a method for constructing global approximations to correlation functions of strongly interacting quantum field theories, starting from perturbative results. The key idea is to employ interpolation method, such as the two-point…
Histopolation, or interpolation on segments, is a mathematical technique used to approximate a function $f$ over a given interval $I=[a,b]$ by exploiting integral information over a set of subintervals of $I$. Unlike classical polynomial…
We develop new methods for approximating conformal blocks as positive functions times polynomials, with applications to the numerical bootstrap. We argue that to obtain accurate bootstrap bounds, conformal block approximations should…
This paper provides approximation orders for a class of nonlinear interpolation procedures for univariate data sampled over $\sigma$ quasi-uniform grids. The considered interpolation is built using both essentially nonoscillatory (ENO) and…
Singular and oscillatory functions feature in numerous applications. The high-accuracy approximation of such functions shall greatly help us develop high-order methods for solving applied mathematics problems. This paper demonstrates that…