Digital nets and sequences: discrepancy and quasi-Monte Carlo integration
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 researc...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2010
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| Subjects: | |
| Online Access: | BSB01 FHN01 UPA01 Volltext |
| Summary: | 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xvii, 600 pages) |
| ISBN: | 9780511761188 |
| DOI: | 10.1017/CBO9780511761188 |
Staff View
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| 245 | 1 | 0 | |a Digital nets and sequences |b discrepancy and quasi-Monte Carlo integration |c Josef Dick, Friedrich Pillichshammer |
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| 505 | 8 | |a Machine generated contents note: 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 | |
| 520 | |a 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 | ||
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| 650 | 4 | |a Digital filters (Mathematics) | |
| 700 | 1 | |a Pillichshammer, Friedrich |e Sonstige |0 (DE-588)1059461153 |4 oth | |
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Record in the Search Index
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| author | Dick, Josef |
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| contents | Machine generated contents note: 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511761188 (OCoLC)967603355 (DE-599)BVBBV043944002 |
| dewey-full | 518/.282 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
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| isbn | 9780511761188 |
| language | English |
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| spelling | Dick, Josef Verfasser (DE-588)1168177987 aut Digital nets and sequences discrepancy and quasi-Monte Carlo integration Josef Dick, Friedrich Pillichshammer Digital Nets & Sequences Cambridge Cambridge University Press 2010 1 online resource (xvii, 600 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) Machine generated contents note: 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 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 Monte Carlo method Nets (Mathematics) Sequences (Mathematics) Numerical integration Digital filters (Mathematics) Pillichshammer, Friedrich Sonstige (DE-588)1059461153 oth Erscheint auch als Druck-Ausgabe, Hardcover 978-0-521-19159-3 https://doi.org/10.1017/CBO9780511761188 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Dick, Josef Digital nets and sequences discrepancy and quasi-Monte Carlo integration Machine generated contents note: 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 Monte Carlo method Nets (Mathematics) Sequences (Mathematics) Numerical integration Digital filters (Mathematics) |
| title | Digital nets and sequences discrepancy and quasi-Monte Carlo integration |
| title_alt | Digital Nets & Sequences |
| title_auth | Digital nets and sequences discrepancy and quasi-Monte Carlo integration |
| title_exact_search | Digital nets and sequences discrepancy and quasi-Monte Carlo integration |
| title_full | Digital nets and sequences discrepancy and quasi-Monte Carlo integration Josef Dick, Friedrich Pillichshammer |
| title_fullStr | Digital nets and sequences discrepancy and quasi-Monte Carlo integration Josef Dick, Friedrich Pillichshammer |
| title_full_unstemmed | Digital nets and sequences discrepancy and quasi-Monte Carlo integration Josef Dick, Friedrich Pillichshammer |
| title_short | Digital nets and sequences |
| title_sort | digital nets and sequences discrepancy and quasi monte carlo integration |
| title_sub | discrepancy and quasi-Monte Carlo integration |
| topic | Monte Carlo method Nets (Mathematics) Sequences (Mathematics) Numerical integration Digital filters (Mathematics) |
| topic_facet | Monte Carlo method Nets (Mathematics) Sequences (Mathematics) Numerical integration Digital filters (Mathematics) |
| url | https://doi.org/10.1017/CBO9780511761188 |
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