Functions of bounded variation in numerical integration

In this talk I present the key idea underlying modern quasi-Monte Carlo integration rules. The Koksma - Hlawka Theorem connects number theory with functional analysis and establishes a powerful method for the approximation of integrals of real-valued functions.

Leaving number theory aside, I plan to focus on the analytical part of the theorem. In particular I present a new concept of bounded variation of multi-dimensional functions yielding a general version of the Theorem of Koksma - Hlawka .

One strength of this new concept is that the corresponding spaces of functions of bounded variation have nice algebraic properties and include various discontinuous functions in a natural way. I will illustrate these results on concrete integration problems from integral geometry and stereology .

This is a joint work with Anne Marie Svane .