What is the 'most uniform' way of distributing n points in the unit square? How big is the 'irregularity' necessarily present in any such distribution? Such questions are treated in geometric discrepancy theory. The book is an accessible and lively introduction to this area, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research. Including a wide variety of mathematical techniques (from harmonic analysis, combinatorics, algebra etc.) in action on non-trivialexamples, the book is suitable for a 'special topic' course for early graduates in mathematics and computer science. Besides professional mathematicians, it will be of interest to specialists in fields where a large collection of objects should be 'uniformly' represented by a smaller sample (such as high-dimensional numerical integration in computational physics or financial mathematics, efficient divide-and-conquer algorithms in computer science, etc.). Only up-to-date comprehensive guide to the subject INDICE: Introduction.- Low-Discrepancy Sets for Axis-Parallel Boxes.- Upper Bounds in the Lebesgue-Measure Setting.- Combinatorial Discrepancy.- VC-Dimension and Discrepancy.- Lower Bounds.- More Lower Bounds and the Fourier Transform.- Tables of Selected Discrepancy Bounds.- Bibliography.- Index.- Hints.
- ISBN: 978-3-642-03941-6
- Editorial: Springer
- Encuadernacion: Rústica
- Páginas: 296
- Fecha Publicación: 01/11/2009
- Nº Volúmenes: 1
- Idioma: Inglés