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| Detailed information |
| Original study plan |
Master's programme Computer Mathematics 2021W |
| Objectives |
The problem of numerical integration occurs in many practical applications. These range from computational mathematics, finance, statistics, and computer graphics to life sciences, to name just a few areas where integrals or expected values have to be computed. In most cases this cannot be done analytically, and one has to resort to numerical methods.
One popular, modern and very powerful method in this context is the so-called quasi-Monte Carlo (QMC) method that is, in a nutshell, a deterministic version of the Monte Carlo method and that is based on number theoretic concepts. Two important instances of these are the method of good lattice points and rules based on digital nets, which are both in the core of this lecture. We learn how to construct such integration rules and analyze their quality from several aspects.
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| Subject |
The following topics are discussed: general introduction to the Monte Carlo and quasi-Monte Carlo method, uniform distribution modulo one discrepancy theory, error analysis in reproducing kernel Hilbert spaces, constructions of QMC rules (lattice methods, digital nets, Halton sequences), dependence of the error bounds on the dimension, avoiding the curse of dimensionality.
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| Criteria for evaluation |
Oral exam
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| Methods |
Blackboard presentation
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| Language |
English |
| Study material |
- Lecture notes;
- For further reading we recommend:
- H. Niederreiter and A. Winterhof: Applied Number Theory
- G. Leobacher and F. Pillichshammer: Introduction to quasi-Monte Carlo Integration and Applications
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| Changing subject? |
No |
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