Format:
Online-Ressource (XIV, 296 pages with 96 illustrations, digital)
ISBN:
9783642039423
Series Statement:
Algorithms and Combinatorics 18
Content:
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.
Content:
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-trivial examples, 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.). From the reviews: "...The numerous illustrations are well placed and instructive. The clear and elegant exposition conveys a wealth of intuitive insights into the techniques utilized. Each section usually consists of text, historical remarks and references for the specialist, and exercises. Hints are provided for the more difficult exercises, with the exercise-hint format permitting inclusion of more results than otherwise would be possible in a book of this size..." Allen D. Rogers, Mathematical Reviews Clippings (2001) .
Note:
Description based upon print version of record
,
Preface to the Second Printing; Preface; Table of Contents; Notation; 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; News Scan 1999--2009; Bibliography; Index; Hints
Additional Edition:
ISBN 9783642039416
Additional Edition:
Buchausg. u.d.T. Matoušek, Jiří, 1963 - 2015 Geometric discrepancy Berlin : Springer, 2010 ISBN 9783642039416
Language:
English
Subjects:
Mathematics
Keywords:
Diskrepanz
;
Punktverteilungsproblem
;
Diskrepanz
;
Punktverteilungsproblem
DOI:
10.1007/978-3-642-03942-3
URL:
Volltext
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URL:
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