250091 VO Number theoretic methods in numerical analysis (2024S)

In this lecture, we will develop the fundamental theoretical results underlying the quasi-Monte Carlo method for numerical integration, including the concepts of uniform distribution modulo 1 and discrepancy. In particular, for a chosen, finite point set in the domain of integration, we can bounded the integration error of the quasi-Monte Carlo (QMC) method by a quantity depending solely on the smoothness of the function to be integrated and the discrepancy of the point set (the Koksma-Hlawka inequality). As a consequence, point sets (and sequences) that have low discrepancy are crucial for successful application of QMC. Hence, we will also study some of the most important construction rules for low discrepancy sets.

Note: The lecture will be held in English language.