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

by JosefDick (Author), Friedrich Pillichshammer (Author)

New
Hardcover
2010
$127.85

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.

Synopsis

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.

$127.85

Quantity

20+ in stock

More Information

Format: Hardcover
Pages: 618
Publisher: Cambridge University Press
Published: 09 Sep 2010
ISBN 10: 0521191599
ISBN 13: 9780521191593

Media 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

Author Bio

Josef Dick is a lecturer in the School of Mathematics and Statistics at the University of New South Wales, Australia. Friedrich Pillichshammer is a Professor in the Institute for Financial Mathematics at the University of Linz, Austria.