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Explicit constructions of point sets with the best possible order of L2-discrepancy by Dick, Josef; Pillichshammer, Friedrich is a scholarly article available to read on EtoBox.

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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

Author

Dick, Josef; Pillichshammer, Friedrich

Publisher

Cambridge University Press (Virtual Publishing)

Published

2010

Language

EN

ISBN

9780511798825