Concepts and implementation of the Cuba library for multidimensional numerical integration are elucidated. 1. Overview Cuba [1] is a library for multidimensional numerical integration. It features four integration algorithms with interfaces for Fortran, C/C++, and Mathematica. All four can integrate vector integrands and their invocation is quite similar to make it easy to switch routines for c...

Monte Carlo integration with variance reduction by means of control variates can be implemented the ordinary least squares estimator for intercept in a multiple linear regression model integrand as response and covariates. Even without special knowledge on integrand, significant efficiency gains obtained if variate space is sufficiently large. Incorporating large number procedure may however re...

Here we will begin by deriving the basic trapezoidal and Simpson’s integration formulas for functions that can be evaluated at all points in the integration range, i.e, there are no singularities in this range. We will also show how the remaining discretization errors present in these low-order formulas can be systematically extrapolated away to arbitrarily high order; a method known as Romberg...

s A numerical iterative scheme is suggested to solve the Euler equations in two and three dimensions. The step of the iteration procedure consists of integration over the velocity which is here carried out by three di erent approximate integration methods, and in particular, by a special Monte Carlo technique. Regarding the Monte Carlo integration, we suggest a dependent sampling technique whic...

Numerical integration is fundamental in multiple Monte Carlo rendering problems. We present a sample reweighting scheme, including underlying theory, and analysis of numerical performance for the an unknown one-dimensional function. Our method simple to implement builds upon insight link weights function reconstruction process during integration. provide proof that our solution unbiased cases c...

introduction : due to the importance of laser light penetration and propagation in biological tissues, many researchers have proposed several numerical methods such as monte carlo, finite element and green function methods. among them, the monte carlo method is an accurate method which can be applied for different tissues. however, because of its statistical nature, monte carlo simulation requi...

While the Quasi-Monte Carlo method of numerical integration achieves smaller integration error than standard Monte Carlo, its use in particle physics phenomenology has been hindered by the abscence of a reliable way to estimate that error. The standard Monte Carlo error estimator relies on the assumption that the points are generated independently of each other and, therefore, fails to account ...