Related papers: One class of integrals evaluation in magnet solito…
It is well known that, using fast algorithms for polynomial multiplication and division, evaluation of a polynomial $F \in \mathbb{C}[x]$ of degree $n$ at $n$ complex-valued points can be done with $\tilde{O}(n)$ exact field operations in…
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
Author presents a study of certain category of the integrals, which might look quite difficult to compute, but in fact are easily computable, because they do not depend on the parameter in the integrand. As simple and elementary the…
Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
The classical Langevin Monte Carlo method looks for samples from a target distribution by descending the samples along the gradient of the target distribution. The method enjoys a fast convergence rate. However, the numerical cost is…
In our quest for the design, the analysis and the implementation of a subdivision algorithm for finding the complex roots of univariate polynomials given by oracles for their evaluation, we present sub-algorithms allowing substantial…
Magnetic quadrupoles are essential components of particle accelerators like the Large Hadron Collider. In order to study numerically the stability of the particle beam crossing a quadrupole, a large number of particle revolutions in the…
The standard procedure when evaluating integrals of a given family of Feynman integrals, corresponding to some Feynman graph, is to construct an algorithm which provides the possibility to write any particular integral as a linear…
An operatorial method, already employed to formulate a generalization of the Ramanujan master theorem, is applied to the evaluation of integrals of various type. This technique provide a very flexible and powerful tool yielding new results…
We propose to store several integers modulo a small prime into a single machine word. Modular addition is performed by addition and possibly subtraction of a word containing several times the modulo. Modular Multiplication is not directly…
An accurate method to compute enclosures of Abelian integrals is developed. This allows for an accurate description of the phase portraits of planar polynomial systems that are perturbations of Hamiltonian systems. As an example, it is…
We cover some useful techniques in computational aspects of analytic number theory, with specific emphasis on ideas relevant to the evaluation of L-functions. These techniques overlap considerably with basic methods from analytic number…
An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.
We present a new method for evaluating tensor integrals in the large-scale structure. Decomposing a $\Lambda$CDM-like universe into a finite sum of scaling universes using the FFTLog, we can recast loop integrals for biased tracers in the…
Group Theory techniques can aid greatly the determination of magnetic structures. The integration of their calculations into new and existing refinement programs is an ongoing development that will simplify and make more rigorous the…
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities. The focus is on accurate and efficient numerical approximations of their solutions, which will be defined via the laws of…