Related papers: An efficient algorithm for accelerating the conver…
An important step in the efficient computation of multi-dimensional theta functions is the construction of appropriate symplectic transformations for a given Riemann matrix assuring a rapid convergence of the theta series. An algorithm is…
Higher-order tensor methods were recently proposed for minimizing smooth convex and nonconvex functions. Higher-order algorithms accelerate the convergence of the classical first-order methods thanks to the higher-order derivatives used in…
We define a parametric variant of generalized Euler sums and construct contour integration to give some explicit evaluations of these parametric Euler sums. In particular, we establish several explicit formulas of (Hurwitz) zeta functions,…
We present Cahn-Hilliard and Allen-Cahn numerical integration algorithms that are unconditionally stable and so provide significantly faster accuracy-controlled simulation. Our stability analysis is based on Eyre's theorem and unconditional…
Integrals involving the kernel function $sech (\pi x)$ over a semi-infinite range are of general interest in the study of Riemann's function $\zeta(s)$ and Hurwitz' function $\zeta(s,a)$. Such integrals that include the $arctan$ and $log$…
The solution of linear systems of equations is a very frequent operation and thus important in many fields. The complexity using classical methods increases linearly with the size of equations. The HHL algorithm proposed by Harrow et al.…
We develop ladders that reduce $\zeta(n):=\sum_{k>0}k^{-n}$, for $n=3,5,7,9,11$, and $\beta(n):=\sum_{k\ge0}(-1)^k(2k+1)^{-n}$, for $n=2,4,6$, to convergent polylogarithms and products of powers of $\pi$ and $\log2$. Rapid computability…
The main aim of this paper is to give a new generalization of Hurwitz-Lerch Zeta function of two variables.Also, we investigate several interesting properties such as integral representations, summation formula and a connection with…
Based on the Beylkin-Cramer summation rule, we introduce a new fast algorithm that enable us to explore the high order statistics efficiently in large data sets. Central to this technique is to make decomposition both of fields and…
Using a different approach, we derive integral representations for the Riemann zeta function and its generalizations (the Hurwitz zeta, $\zeta(-k,b)$, the polylogarithm, $\mathrm{Li}_{-k}(e^m)$, and the Lerch transcendent,…
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…
In this article a unified approach to iterative soft-thresholding algorithms for the solution of linear operator equations in infinite dimensional Hilbert spaces is presented. We formulate the algorithm in the framework of generalized…
This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given.…
The numerical matrix Numerov algorithm is used to solve the stationary Schr\"odinger equation for central Coulomb potentials. An efficient approximation for accelerating the convergence is proposed. The Numerov method is error-prone if the…
This paper develops an efficient algorithm for computing the Euclidean projection onto the top-k-sum constraint, a key operation in financial risk management and matrix optimization problems. Existing projection methods rely on sorting and…
The phase retrieval problem is found in various areas of applications of engineering and applied physics. It is also a very active field of research in mathematics, signal processing and machine learning. In this paper, we present an…
Five series are evaluated in terms of zeta values. Three of the series involve harmonic numbers and one involves Stirling numbers of the first kind. The evaluation of these series is reduced to the evaluation of certain integrals, including…
Building upon the efficient implementation of hybrid density functionals (HDFs) for large-scale periodic systems within the framework of numerical atomic orbital bases using the localized resolution of identity (RI) technique, we have…
This report introduces new series and variations of some hypergeometric type identities for fast computing of logarithms $\log\,p$ for small positive integers $p$. These series were found using Wilf Zeilberger (WZ) method and/or integer…
Distributed network optimization has been studied for well over a decade. However, we still do not have a good idea of how to design schemes that can simultaneously provide good performance across the dimensions of utility optimality,…