Related papers: Identities for the arctangent function by enhanced…
The combination of integrability and crossing symmetry has proven to give tight non-perturbative bounds on some planar structure constants in $\mathcal{N}$=4 SYM, particularly in the setup of defect observables built on a Wilson-Maldacena…
In this paper we present a new family of rules for numerical integration. This family has up to half the error of the widely used Newton-Cotes rules when a sufficient number of points is evaluated and also much better numerical stability…
Myocardial perfusion imaging (MPI) with single-photon emission computed tomography (SPECT) is a widely used and cost-effective diagnostic tool for coronary artery disease. However, the lengthy scanning time in this imaging procedure can…
Machin-like arctangent relations are classical tools for computing $\pi$, with efficiency quantified by the Lehmer measure ($\lambda$). We present a framework for discovering low-measure relations by coupling the PSLQ integer-relation…
Monte Carlo integration is a commonly used technique to compute intractable integrals and is typically thought to perform poorly for very high-dimensional integrals. To show that this is not always the case, we examine Monte Carlo…
We establish strong-type endpoint $L^p(\mathbb R^d) \to L^q(\mathbb R^d)$ bounds for the operator given by convolution with affine arclength measure on polynomial curves for $d \geq 4$. The bounds established depend only on the dimension…
In this paper, we consider the integrating factor midpoint method for wave-type equations and derive optimal order a posteriori error estimates. We first introduce an integrating factor midpoint approximation defined by the piecewise linear…
Numerically estimating the integral of functions in high dimensional spaces is a non-trivial task. A oft-encountered example is the calculation of the marginal likelihood in Bayesian inference, in a context where a sampling algorithm such…
Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$…
In this paper, we propose and study a fast multilevel dimension iteration (MDI) algorithm for computing arbitrary $d$-dimensional integrals based on tensor product approximations. It reduces the computational complexity (in terms of the CPU…
The accuracy of the numerical solution of a fractional differential equation depends on the differentiability class of the solution. The derivatives of the solutions of fractional differential equations often have a singularity at the…
Integration by parts identities (IBPs) can be used to express large numbers of apparently different d-dimensional Feynman Integrals in terms of a small subset of so-called master integrals (MIs). Using the IBPs one can moreover show that…
Arb is a C library for arbitrary-precision interval arithmetic using the midpoint-radius representation, also known as ball arithmetic. It supports real and complex numbers, polynomials, power series, matrices, and evaluation of many…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
In this paper we present a methodology for increasing the accuracy and accelerating the convergence of numerical methods for solution of Maxwell's equations in the frequency domain by taking into account the be-havior of the electromagnetic…
We present a simple recurrent formula to generate the Machin-like expression for calculating $\pi/4$. The method works for any denominator in the starting term and always provides a finite decomposition. We show that the terms in the…
It is by now well established that, by means of the integration by part identities, all the integrals occurring in the evaluation of a Feynman graph of given topology can be expressed in terms of a few independent master integrals. It is…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Piecewise affine functions are widely used to approximate nonlinear and discontinuous functions. However, most, if not all existing models only deal with fitting continuous functions. In this paper, we investigate the problem of fitting a…
Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…