Digital Nets and Sequences : Discrepancy Theory and Quasi-Monte Carlo Integration - Josef Dick

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Digital Nets and Sequences

Discrepancy Theory and Quasi-Monte Carlo Integration

By: Josef Dick, Friedrich Pillichshammer

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Hardcover | 9 September 2010

At a Glance

Hardcover
620 Pages

Edition Type
New edition

Dimensions(cm)
24.41 x 16.99 x 3.33

Hardcover

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Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasiâ"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, quasiâ"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.

Industry Reviews

"It will give readers the confidence that their estimates of variance are tractable, and they can therefore use quasi-Monte Carlo (QMC) integration to do the software engineering tradeoff analysis that is critical to professional software project management and architecture. This textbook--and believe me, it is a textbook--will lead students to a deep understanding of the potential errors that can be expected." Larry Bernstein, Computing Reviews
"This book provides a self-contained and comprehensive exposition of one of the most attractive techniques for numerical integration, the so-called quasi-Monte Carlo (QMC) rule. As well-known specialists in the field, the authors have made a tour de force to include, systematize, and unify their achievements and an impressive number of results of other people. By introducing the concepts and methods in an accessible and intuitive form, the authors have provided a useful book that is accompanied by a lot of illustrative examples, graphics and applications." Petru P. Blaga, Mathematical Reviews

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You Can Find This Book In

Non-Fiction Computing & I.T.Computer Programming & Software Development Algorithms & Data Structures Mathematics Calculus & Mathematical Analysis Numerical Analysis Probability & Statistics Computer Science

Preface
Notation
Introduction
Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces
Geometric discrepancy
Nets and sequences
Discrepancy estimates and average type results
Connections to other discrete objects
Duality Theory
Special constructions of digital nets and sequences
Propagation rules for digital nets
Polynomial lattice point sets
Cyclic digital nets and hyperplane nets
Multivariate integration in weighted Sobolev spaces
Randomisation of digital nets
The decay of the Walsh coefficients of smooth functions
Arbitrarily high order of convergence of the worst-case error
Explicit constructions of point sets with best possible order of L2-discrepancy
Walsh functions
Algebraic function fields
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

Digital Nets and Sequences

Discrepancy Theory and Quasi-Monte Carlo Integration

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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