- know and understand the fundamentals of Monte Carlo and quasi-Monte Carlo methods
- know and understand basic concepts from the theory of uniform distribution and discrepancy
- know the fundamental error estimate from Koksma and Hlawka and to be able to prove this result
- know important constructions of quasi-Monte Carlo point sets
- know the methods of lattice rules and digital nets and be able to work with this methods
- be able to make a worst-case error analysis for simple examples of reproducing kernel Hilbert spaces independently
|
Monte Carlo method, numerical integration, uniform distribution and Weyl's criterion, discrepancy, Koksma-Hlawka inequality, worst-case error, error analysis in Hilbert spaces with reproducing kernel, quasi-Monte Carlo method, lattice rules, digital nets, curse of dimension and tractability
|
