Geometric Discrepancy

An Illustrated Guide
1. Auflage 1999. 2. printing 2009
ISBN: 978-3-642-03941-6
Verlag: Springer

Buch, Englisch, Band 18, 289 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 464 g

Reihe: Algorithms and Combinatorics

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? This book is an accessible and lively introduction to the area of geometric discrepancy theory, with numerous exercises and illustrations. In separate, more specialized parts, it also provides a comprehensive guide to recent research.

Zielgruppe

Research

Autoren/Hrsg.

Matousek, Jiri

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Geometrie Geometrie der modernen Physik
• Mathematik | Informatik Mathematik Operations Research Graphentheorie

Inhaltsverzeichnis

1. Introduction.- 2. Low-Discrepancy Sets for Axis-Parallel Boxes.- 3. Upper Bounds in the Lebesgue-Measure Setting.- 4. Combinatorial Discrepancy.- 5. VC-Dimension and Discrepancy.- 6. Lower Bounds.- 7. More Lower Bounds and the Fourier Transform.- A. Tables of Selected Discrepancy Bounds.- Hints.