An introduction to contemporary quasi Monte Carlo methods, digital nets and sequences, and discrepancy theory. Includes many exercises, examples and illustrations.
An introduction to contemporary quasi Monte Carlo methods, digital nets and sequences, and discrepancy theory. Includes many exercises, examples and illustrations.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Josef Dick is a lecturer in the School of Mathematics and Statistics at the University of New South Wales, Australia.
Inhaltsangabe
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.
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.
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