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Geometric Discrepancy

2009-12-02 Mathematics
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Release : 2009-12-02
Genre : Mathematics
Kind : eBook
Book Rating : 421/5 ( reviews)

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Book Synopsis Geometric Discrepancy by : Jiri Matousek

Download or read book Geometric Discrepancy written by Jiri Matousek. This book was released on 2009-12-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Discrepancy Theory

2020-01-20 Mathematics
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Release : 2020-01-20
Genre : Mathematics
Kind : eBook
Book Rating : 203/5 ( reviews)

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Book Synopsis Discrepancy Theory by : Dmitriy Bilyk

Download or read book Discrepancy Theory written by Dmitriy Bilyk. This book was released on 2020-01-20. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory

A Panorama of Discrepancy Theory

2014-10-07 Mathematics
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Release : 2014-10-07
Genre : Mathematics
Kind : eBook
Book Rating : 969/5 ( reviews)

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Book Synopsis A Panorama of Discrepancy Theory by : William Chen

Download or read book A Panorama of Discrepancy Theory written by William Chen. This book was released on 2014-10-07. Available in PDF, EPUB and Kindle. Book excerpt: This is the first work on Discrepancy Theory to show the present variety of points of view and applications covering the areas Classical and Geometric Discrepancy Theory, Combinatorial Discrepancy Theory and Applications and Constructions. It consists of several chapters, written by experts in their respective fields and focusing on the different aspects of the theory. Discrepancy theory concerns the problem of replacing a continuous object with a discrete sampling and is currently located at the crossroads of number theory, combinatorics, Fourier analysis, algorithms and complexity, probability theory and numerical analysis. This book presents an invitation to researchers and students to explore the different methods and is meant to motivate interdisciplinary research.

Discrepancy Theory

2020-01-20 Mathematics
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Release : 2020-01-20
Genre : Mathematics
Kind : eBook
Book Rating : 587/5 ( reviews)

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Book Synopsis Discrepancy Theory by : Dmitriy Bilyk

Download or read book Discrepancy Theory written by Dmitriy Bilyk. This book was released on 2020-01-20. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this book focus on a variety of topics related to discrepancy theory, comprising Fourier techniques to analyze discrepancy, low discrepancy point sets for quasi-Monte Carlo integration, probabilistic discrepancy bounds, dispersion of point sets, pair correlation of sequences, integer points in convex bodies, discrepancy with respect to geometric shapes other than rectangular boxes, and also open problems in discrepany theory.

Digital Nets and Sequences

2010-09-09 Computers
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Release : 2010-09-09
Genre : Computers
Kind : eBook
Book Rating : 052/5 ( reviews)

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Book Synopsis Digital Nets and Sequences by : Josef Dick

Download or read book Digital Nets and Sequences written by Josef Dick. This book was released on 2010-09-09. Available in PDF, EPUB and Kindle. Book excerpt: Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi–Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.

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