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

Publisher: 
Cambridge University Press
Number of Pages: 
600
Price: 
85.00
ISBN: 
9780521191593
Date Received: 
Wednesday, November 10, 2010
Reviewable: 
Include In BLL Rating: 
Reviewer Email Address: 
Josef Dick and Friedrich Pillichshammer
Publication Date: 
2010
Format: 
Hardcover
Category: 
Textbook

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.

Publish Book: 
Modify Date: 
Wednesday, January 12, 2011

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