High Performance Numerical Computing for High Energy Physics: A New Challenge for Big Data Science

Table 1

Efficiency of integration methods for 1 dimension and for 𝑑 dimensions.

Method	1 dimension	𝑑 dimensions
Monte Carlo	𝑛^−1/2	𝑛^−1/2
Trapezoidal rule	𝑛^−2	𝑛^−2/𝑑
Simpson’s rule	𝑛^−4	𝑛^−4/𝑑
𝑚-points Gauss rule (𝑚<𝑛)	𝑛^−2𝑚	𝑛^−2𝑚/𝑑