000			03311nam a22003978i 4500
001			CR9780511761188
003			UkCbUP
005			20200124160302.0
006			m|||||o||d||||||||
007			cr||||||||||||
008			100506s2010||||enk o ||1 0|eng|d
020			_a9780511761188 (ebook)
020			_z9780521191593 (hardback)
040			_aUkCbUP _beng _erda _cUkCbUP
050	0	0	_aQA298 _b.D53 2010
082	0	0	_a518/.282 _222
100	1		_aDick, J. _q(Josef), _eauthor.
245	1	0	_aDigital nets and sequences : _bdiscrepancy and quasi-Monte Carlo integration / _cJosef Dick, Friedrich Pillichshammer.
246	3		_aDigital Nets & Sequences
264		1	_aCambridge : _bCambridge University Press, _c2010.
300			_a1 online resource (xvii, 600 pages) : _bdigital, PDF file(s).
336			_atext _btxt _2rdacontent
337			_acomputer _bc _2rdamedia
338			_aonline resource _bcr _2rdacarrier
500			_aTitle from publisher's bibliographic system (viewed on 05 Oct 2015).
505	8		_aMachine 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			_aIndispensable 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.
650		0	_aMonte Carlo method.
650		0	_aNets (Mathematics)
650		0	_aSequences (Mathematics)
650		0	_aNumerical integration.
650		0	_aDigital filters (Mathematics)
700	1		_aPillichshammer, Friedrich, _eauthor.
776	0	8	_iPrint version: _z9780521191593
856	4	0	_uhttps://doi.org/10.1017/CBO9780511761188
999			_c520495 _d520493