Digital Nets and Sequences
Digital Nets and Sequences
Friedrich Pillichshammer, Johannes Kepler Universität Linz
AUD$159.05
exc GSTIndispensable 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.
- Clear exposition includes end-of-chapter exercises, numerous examples and illustrations
- Assumes only basic prerequisites
- Ideal for self-study or advanced undergraduate courses, and great as a reference
Product details
September 2010Adobe eBook Reader
9780511795831
0 pages
0kg
45 b/w illus. 260 exercises
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- 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.
