Digital nets and sequences :: discrepancy and quasi-Monte Carlo integration /
"This book is a comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory which starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of th...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Weitere Verfasser: | |
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
©2010.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "This book is a comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory which 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 llustrations"--Provided by publisher. |
| Beschreibung: | 1 online resource (xvii, 600 pages :) |
| Bibliographie: | Includes bibliographical references (pages 583-596) and index. |
| ISBN: | 9780511901973 0511901976 9780511798825 0511798822 9780511761188 051176118X |
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| 520 | |a "This book is a comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory which 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 llustrations"--Provided by publisher. | ||
| 504 | |a Includes bibliographical references (pages 583-596) and index. | ||
| 505 | 0 | |a Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces -- Geometric discrepancy -- Nets and sequences -- Discrepancy estimates and average type results -- Connections to other discrete objects -- Duality theory -- Special constructions of digital nets and sequences -- Propagation rules for digital nets -- Polynomial lattice point sets -- Cyclic digital nets and hyperplane nets -- Multivariate integration in weighted Sobolev spaces -- Randomisation of digital nets -- The decay of the Walsh coefficients of smooth functions -- Arbitrarily high order of convergence of the worst-case error -- Explicit constructions of point sets with best possible order of L2-discrepancy -- Appendix A. Walsh functions -- Appendix B. Algebraic function fields. | |
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Datensatz im Suchindex
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| adam_text | |
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| author | Dick, J. (Josef) |
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| contents | Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces -- Geometric discrepancy -- Nets and sequences -- Discrepancy estimates and average type results -- Connections to other discrete objects -- Duality theory -- Special constructions of digital nets and sequences -- Propagation rules for digital nets -- Polynomial lattice point sets -- Cyclic digital nets and hyperplane nets -- Multivariate integration in weighted Sobolev spaces -- Randomisation of digital nets -- The decay of the Walsh coefficients of smooth functions -- Arbitrarily high order of convergence of the worst-case error -- Explicit constructions of point sets with best possible order of L2-discrepancy -- Appendix A. Walsh functions -- Appendix B. Algebraic function fields. |
| ctrlnum | (OCoLC)668233138 |
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| dewey-ones | 518 - Numerical analysis |
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| discipline | Mathematik |
| format | Electronic eBook |
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| publisher | Cambridge University Press, |
| record_format | marc |
| spelling | Dick, J. (Josef) https://id.oclc.org/worldcat/entity/E39PCjFWTkmDb6vhj4YpDJhGpP http://id.loc.gov/authorities/names/no2009078306 Digital nets and sequences : discrepancy and quasi-Monte Carlo integration / Josef Dick, Friedrich Pillichshammer. Cambridge ; New York : Cambridge University Press, ©2010. 1 online resource (xvii, 600 pages :) text txt rdacontent computer c rdamedia online resource cr rdacarrier "This book is a comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory which 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 llustrations"--Provided by publisher. Includes bibliographical references (pages 583-596) and index. Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces -- Geometric discrepancy -- Nets and sequences -- Discrepancy estimates and average type results -- Connections to other discrete objects -- Duality theory -- Special constructions of digital nets and sequences -- Propagation rules for digital nets -- Polynomial lattice point sets -- Cyclic digital nets and hyperplane nets -- Multivariate integration in weighted Sobolev spaces -- Randomisation of digital nets -- The decay of the Walsh coefficients of smooth functions -- Arbitrarily high order of convergence of the worst-case error -- Explicit constructions of point sets with best possible order of L2-discrepancy -- Appendix A. Walsh functions -- Appendix B. Algebraic function fields. Print version record. Monte Carlo method. http://id.loc.gov/authorities/subjects/sh85087032 Nets (Mathematics) http://id.loc.gov/authorities/subjects/sh85091044 Sequences (Mathematics) http://id.loc.gov/authorities/subjects/sh85120145 Numerical integration. http://id.loc.gov/authorities/subjects/sh85093246 Digital filters (Mathematics) http://id.loc.gov/authorities/subjects/sh85037977 Monte Carlo Method https://id.nlm.nih.gov/mesh/D009010 Méthode de Monte-Carlo. Réseaux (Mathématiques) Suites (Mathématiques) Intégration numérique. Filtres numériques (Mathématiques) MATHEMATICS Numerical Analysis. bisacsh Digital filters (Mathematics) fast Monte Carlo method fast Nets (Mathematics) fast Numerical integration fast Sequences (Mathematics) fast Electronic books. Pillichshammer, Friedrich. http://id.loc.gov/authorities/names/n2010022880 has work: Digital nets and sequences (Text) https://id.oclc.org/worldcat/entity/E39PCH3b6pCg6QdqjDt4JFG3jP https://id.oclc.org/worldcat/ontology/hasWork Print version: Dick, J. (Josef). Digital nets and sequences. New York NY : Cambridge University Press, 2010 9780521191593 (DLC) 2010015151 (OCoLC)601112925 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=331305 Volltext CBO01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=331305 Volltext |
| spellingShingle | Dick, J. (Josef) Digital nets and sequences : discrepancy and quasi-Monte Carlo integration / Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces -- Geometric discrepancy -- Nets and sequences -- Discrepancy estimates and average type results -- Connections to other discrete objects -- Duality theory -- Special constructions of digital nets and sequences -- Propagation rules for digital nets -- Polynomial lattice point sets -- Cyclic digital nets and hyperplane nets -- Multivariate integration in weighted Sobolev spaces -- Randomisation of digital nets -- The decay of the Walsh coefficients of smooth functions -- Arbitrarily high order of convergence of the worst-case error -- Explicit constructions of point sets with best possible order of L2-discrepancy -- Appendix A. Walsh functions -- Appendix B. Algebraic function fields. Monte Carlo method. http://id.loc.gov/authorities/subjects/sh85087032 Nets (Mathematics) http://id.loc.gov/authorities/subjects/sh85091044 Sequences (Mathematics) http://id.loc.gov/authorities/subjects/sh85120145 Numerical integration. http://id.loc.gov/authorities/subjects/sh85093246 Digital filters (Mathematics) http://id.loc.gov/authorities/subjects/sh85037977 Monte Carlo Method https://id.nlm.nih.gov/mesh/D009010 Méthode de Monte-Carlo. Réseaux (Mathématiques) Suites (Mathématiques) Intégration numérique. Filtres numériques (Mathématiques) MATHEMATICS Numerical Analysis. bisacsh Digital filters (Mathematics) fast Monte Carlo method fast Nets (Mathematics) fast Numerical integration fast Sequences (Mathematics) fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85087032 http://id.loc.gov/authorities/subjects/sh85091044 http://id.loc.gov/authorities/subjects/sh85120145 http://id.loc.gov/authorities/subjects/sh85093246 http://id.loc.gov/authorities/subjects/sh85037977 https://id.nlm.nih.gov/mesh/D009010 |
| title | Digital nets and sequences : discrepancy and quasi-Monte Carlo integration / |
| 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. http://id.loc.gov/authorities/subjects/sh85087032 Nets (Mathematics) http://id.loc.gov/authorities/subjects/sh85091044 Sequences (Mathematics) http://id.loc.gov/authorities/subjects/sh85120145 Numerical integration. http://id.loc.gov/authorities/subjects/sh85093246 Digital filters (Mathematics) http://id.loc.gov/authorities/subjects/sh85037977 Monte Carlo Method https://id.nlm.nih.gov/mesh/D009010 Méthode de Monte-Carlo. Réseaux (Mathématiques) Suites (Mathématiques) Intégration numérique. Filtres numériques (Mathématiques) MATHEMATICS Numerical Analysis. bisacsh Digital filters (Mathematics) fast Monte Carlo method fast Nets (Mathematics) fast Numerical integration fast Sequences (Mathematics) fast |
| topic_facet | Monte Carlo method. Nets (Mathematics) Sequences (Mathematics) Numerical integration. Digital filters (Mathematics) Monte Carlo Method Méthode de Monte-Carlo. Réseaux (Mathématiques) Suites (Mathématiques) Intégration numérique. Filtres numériques (Mathématiques) MATHEMATICS Numerical Analysis. Monte Carlo method Numerical integration Electronic books. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=331305 |
| work_keys_str_mv | AT dickj digitalnetsandsequencesdiscrepancyandquasimontecarlointegration AT pillichshammerfriedrich digitalnetsandsequencesdiscrepancyandquasimontecarlointegration |