An introduction to the numerical solver for multiple integrals

Speaker : Guodong Sun
Date: 15/03/2023
Time: 10:30 am - 11:30 am
Location: Room 4B01


Evaluating multiple integrals is challenging when there exists no simple closed form representations. However, they are frequently encountered in network analysis, such as in queueing theory and stochastic geometry. In this reading group talk, I will introduce the development of numerical integration, namely the line of though from Newton’s Trapezoidal rule to Fourier’s spectrum method and to Gauss-Kronrod quadrature method, in which the latest one is proven to be one of the most efficient for one dimensional(1D) numerical integration. This line of thought inspires numerical multiple integrals. As an example, “Genz-Malik algorithm” will be presented, which is used to solve N-dimensional smooth multiple integrals and is prove to be efficient when the dimension ranges from two (2D) to seven (7D). In addition, I will compare the Genz-Malik algorithm with other solvers, such as iterative one dimensional algorithm and Monte Carlo integration.