Related papers: pylevin: Efficient numerical integration of integr…
We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…
We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of functions to Gaussians.
We consider random variables of the form $F=f(V_1,...,V_n)$, where $f$ is a smooth function and $V_i,i\in\mathbb{N}$, are random variables with absolutely continuous law $p_i(y) dy$. We assume that $p_i$, $i=1,...,n$, are piecewise…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
We propose a third-order numerical integrator based on the Neumann series and the Filon quadrature, designed mainly for highly oscillatory partial differential equations. The method can be applied to equations that exhibit small or moderate…
Improving the robustness of neural nets in regression tasks is key to their application in multiple domains. Deep learning-based approaches aim to achieve this goal either by improving their prediction of specific values (i.e., point…
We obtain integral representations of the $n$-th derivatives of the Bessel functions with respect to the order. The numerical evaluation of these expressions is very efficient using a double exponential integration strategy. Also, from the…
This work proposes a framework of benchmark functions designed to facilitate the creation of test cases for numerical optimisation techniques. The framework, written in Python 3, is designed to be easy to install, use, and expand. The…
In this paper, we consider the Clenshaw-Curtis-Filon method for the highly oscillatory Bessel transform $\int_0^1x^\alpha (1-x)^\beta f(x) J_{\nu}(\omega x)dx$, where $f$ is a smooth function on $[0, 1]$, and $\nu\geq0.$ The method is based…
Ensemble-averaged polydisperse bubbly flow models require statistical moments of the evolving bubble size distribution. Under step forcing, these moments reach statistical equilibrium in finite time. However, the transitional phase before…
In this paper, a new python package (optipoly) is described that solves box-constrained optimization problem over multivariate polynomial cost functions. The principle of the algorithm is described before its performance is compared to…
We present peapods (github.com/PeaBrane/peapods), an open-source Python package for Monte Carlo simulation of Ising spin systems with arbitrary coupling constants on periodic Bravais lattices with user-specified neighbor offsets. The…
We consider the problem of symbolic-numeric integration of symbolic functions, focusing on rational functions. Using a hybrid method allows the stable yet efficient computation of symbolic antiderivatives while avoiding issues of…
We consider the path approximation of Bessel processes and develop a new and efficient algorithm. This study is based on a recent work by the authors, on the path approximation of the Brownian motion, and on the construction of specific own…
We present a Python module named PyCheb, to solve the ordinary differential equations by using spectral collocation method. PyCheb incorporates discretization using Chebyshev points, barycentric interpolation and iterate methods. With this…
An algorithm for integration of polynomial functions with variable weight is considered. It provides extension of the Gaussian integration, with appropriate scaling of the abscissas and weights. Method is a good alternative to usually…
For a function that is analytic on and around an interval, Chebyshev polynomial interpolation provides spectral convergence. However, if the function has a singularity close to the interval, the rate of convergence is near one. In these…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal…
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two…