相关论文: A new method to sum divergent power series: educat…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
We establish asymptotic estimates for the least upper bounds of approximations in the uniform metric by Fourier sums of order $n-1$ of classes of $2\pi$-periodic Weyl--Nagy differentiable functions, $W^r_{\beta,p}, 1\le p\le \infty,…
In the \emph{graph matching} problem we observe two graphs $G,H$ and the goal is to find an assignment (or matching) between their vertices such that some measure of edge agreement is maximized. We assume in this work that the observed pair…
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
We propose a new stochastic gradient method for optimizing the sum of a finite set of smooth functions, where the sum is strongly convex. While standard stochastic gradient methods converge at sublinear rates for this problem, the proposed…
This review is focused on the borderline region of theoretical physics and mathematics. First, we describe numerical methods for the acceleration of the convergence of series. These provide a useful toolbox for theoretical physics which has…
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.…
In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derived algorithm and…
In this paper we present a method to derive Pi(x) and other Arithemtical functions that can be generated by a Dirichlet series by variational principles,we use a variational method to determine the solution for a Fredholm integral equation…
The conformal mapping of the Borel plane can be utilized for the analytic continuation of the Borel transform to the entire positive real semi-axis and is thus helpful in the resummation of divergent perturbation series in quantum field…
An adaptive scheme to generate reduced-order models for parametric nonlinear dynamical systems is proposed. It aims to automatize the POD-Greedy algorithm combined with empirical interpolation. At each iteration, it is able to adaptively…
In this paper, we investigate the asymptotics of a class of weighted sums over multiplicative functions and apply our results to deduce a stronger asymptotic form of Yitang Zhang's smoothened GPY sieve with coefficient expressions that are…
Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…
We study the applicability of Pade Approximants (PA) to estimate a "sum" of asymptotic series of the type appearing in QCD. We indicate that one should not expect PA to converge for positive values of the coupling constant and propose to…
We will generalize the combinatorial algorithms for computing $\pi(x)$ to compute sums ${F(x) = \sum_{p \leq x} p^k}$ for $k \in \mathbb{Z}_{\geq 0}$. The detailed exposition of algorithms is included along with implementation details.
Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations,…
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of…
We propose a method for estimating the Fisher score--the gradient of the log-likelihood with respect to model parameters--using score matching. By introducing a latent parameter model, we show that the Fisher score can be learned by…
The frame algorithm uses a simple recursive formula to approximate an unknown vector from its frame coefficients. This note introduces an adaptive version of the frame algorithm that maximizes the error reduction between steps in terms of…
We discuss a new approach of scalar field theory where the small field contributions are treated perturbatively and the large field configurations (which are responsible for the asymptotic behavior of the perturbative series) are neglected.…