Related papers: A Simple approach for precision calculation of Bet…
This paper offers a review of numerical methods for computation of the eigenvalues of Hermitian matrices and the singular values of general and some classes of structured matrices. The focus is on the main principles behind the methods that…
The resummation of logarithmically-enhanced terms to all perturbative orders is a prerequisite for many studies of QCD final-states. Until now such resummations have always been performed by hand, for a single observable at a time. In this…
We present an improved calculation of higher-order corrections to the one-loop self energy of 2P states in hydrogen-like systems with small nuclear charge Z. The method is based on a division of the integration with respect to the photon…
By working out the Bethe sum rule, a boundary condition that takes the form of a linear equality is derived for the fine structure observed in ionization edges present in electron energy-loss spectra. This condition is subsequently used as…
Hedin's $GW$ approximation to the electronic self-energy has been impressively successful to calculate quasiparticle energies, such as ionization potentials, electron affinities, or electronic band structures. The success of this fairly…
We uncover a method of calculation that proceeds at every step without fixing the gauge or specifying details of the regularisation scheme. Results are obtained by iterated use of integration by parts and gauge invariance identities.…
We describe and analyze a numerical algorithm for computing the homology (Betti numbers and torsion coefficients) of semialgebraic sets given by Boolean formulas. The algorithm works in weak exponential time. This means that outside a…
We describe a practical algorithm for computing the Stokes multipliers of a linear differential equation with polynomial coefficients at an irregular singular point of single level one. The algorithm follows a classical approach based on…
We summarize results for the complete one-loop electroweak logarithmic corrections for general processes at high energies and fixed angles. Our results are applicable to arbitrary matrix elements that are not mass-suppressed. We give…
We develop a numerical homogenization method for fourth-order singular perturbation problems within the framework of heterogeneous multiscale method. These problems arise from heterogeneous strain gradient elasticity and elasticity models…
In this article, we show new effective approximation measures for the shifted logarithm of algebraic numbers which belong to a number field of arbitrary degree. Our measures refine previous ones including those for usual logarithms. We…
We present the numerical analysis of a finite element method (FEM) for one-dimensional Dirichlet problems involving the logarithmic Laplacian (the pseudo-differential operator that appears as a first-order expansion of the fractional…
Constant potential molecular dynamics simulation plays important role for applications of electrochemical systems, yet the calculation of charge fluctuation on electrodes remains a computational bottleneck. We propose a highly scalable,…
Many iterative algorithms in optimization, computational geometry, computer algebra, and other areas of computer science require repeated computation of some algebraic expression whose input changes slightly from one iteration to the next.…
This paper presents RevOrder, a novel technique aimed at improving arithmetic operations in large language models (LLMs) by reversing the output digits in addition, subtraction, and n-digit by 1-digit (nD by 1D) multiplication tasks. Our…
For many observables, the most difficult part of a single logarithmic resummation is the analytical treatment of the observable's dependence on multiple emissions. We present a general numerical method, which allows the resummation…
We perform highly accurate calculations of the leading order QED correction to the ground electronic state of molecular hydrogen. Numerical results are obtained for a grid of the internuclear distances $R=0-10$ au with the relative…
We introduce new rounding methods to improve the accuracy of finite precision quantum arithmetic. These quantum rounding methods are applicable when multiple samples are being taken from a quantum program. We show how to use multiple…
We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the $gl(2)$-invariant $R$-matrix for the two-site Bose-Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get…
Power systems are globally experiencing an unprecedented growth in size and complexity due to the advent of nonconventional generation and consumption technologies. To navigate computational complexity, power system dynamic models are often…