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Digital Nets and Sequences : Discrepancy Theory and Quasi–Monte Carlo...

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Specificaties

Objectstaat
Vrijwel nieuw: Een boek dat er als nieuw uitziet, maar al wel is gelezen. De kaft is niet zichtbaar ...
ISBN
9780521191593
Publication Name
Digital Nets and Sequences : Discrepancy Theory and Quasi–Monte Carlo Integration
Item Length
10in
Publisher
Cambridge University Press
Publication Year
2010
Type
Textbook
Format
Hardcover
Language
English
Item Height
1.4in
Author
Friedrich Pillichshammer, Josef Dick
Features
New Edition
Item Width
7.1in
Item Weight
42.3 Oz
Number of Pages
618 Pages

Over dit product

Product Information

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.

Product Identifiers

Publisher
Cambridge University Press
ISBN-10
0521191599
ISBN-13
9780521191593
eBay Product ID (ePID)
84321210

Product Key Features

Author
Friedrich Pillichshammer, Josef Dick
Publication Name
Digital Nets and Sequences : Discrepancy Theory and Quasi–Monte Carlo Integration
Format
Hardcover
Language
English
Features
New Edition
Publication Year
2010
Type
Textbook
Number of Pages
618 Pages

Dimensions

Item Length
10in
Item Height
1.4in
Item Width
7.1in
Item Weight
42.3 Oz

Additional Product Features

Lc Classification Number
Qa298 .D53 2010
Edition Description
New Edition
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, "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
Table of Content
Preface; Notation; 1. Introduction; 2. Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces; 3. Geometric discrepancy; 4. Nets and sequences; 5. Discrepancy estimates and average type results; 6. Connections to other discrete objects; 7. Duality Theory; 8. Special constructions of digital nets and sequences; 9. Propagation rules for digital nets; 10. Polynomial lattice point sets; 11. Cyclic digital nets and hyperplane nets; 12. Multivariate integration in weighted Sobolev spaces; 13. Randomisation of digital nets; 14. The decay of the Walsh coefficients of smooth functions; 15. Arbitrarily high order of convergence of the worst-case error; 16. Explicit constructions of point sets with best possible order of L2-discrepancy; Appendix A. Walsh functions; Appendix B. Algebraic function fields; References; Index.
Copyright Date
2010
Topic
Functional Analysis, Probability & Statistics / Stochastic Processes, Numerical Analysis, General, Topology
Lccn
2010-015151
Dewey Decimal
518/.282
Intended Audience
Scholarly & Professional
Dewey Edition
22
Illustrated
Yes
Genre
Computers, Mathematics

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