Digital nets and sequences
Subtitle: discrepancy theory and quasi-Monte Carlo integration
By: Josef Dick, Friedrich Pillichshammer
Contributors: Pillichshammer, Friedrich
Publisher: Cambridge University Press
Published: 2010
Place of publication: Cambridge; New York, NY
Language: eng
Number of pages: 600
ISBN-13: 9780521191593
Subjects: Numerical integration; Sequences (Mathematics); Digital filters (Mathematics); Monte Carlo method; Nets (Mathematics)
Description: "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"--
Notes: Includes bibliographical referencs and index.