Digital nets and sequences : discrepancy theory and quasi-Monte Carlo integration

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Digital nets and sequences : discrepancy theory and quasi-Monte Carlo integration / Josef Dick, Friedrich Pillichshammer

資料種別:

図書

出版情報:

Cambridge : Cambridge University Press, 2010

形態:

xvii, 600 p. ; 26 cm

著者名:

ISBN:

9780521191593 [0521191599] (: hbk)

書誌ID:

BB03602827

子書誌情報

フルテキスト

所蔵情報

他の版・巻

書誌詳細

注記:

Includes bibliographical references and index

主題:

推計学．標本分布論

言語:

英語

目次情報:

Preface

Notation

Introduction / 1：

Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces / 2：

Geometric discrepancy / 3：

Nets and sequences / 4：

Discrepancy estimates and average type results / 5：

Connections to other discrete objects / 6：

Duality Theory / 7：

Special constructions of digital nets and sequences / 8：

Propagation rules for digital nets / 9：

Polynomial lattice point sets / 10：

Cyclic digital nets and hyperplane nets / 11：

Multivariate integration in weighted Sobolev spaces / 12：

Randomisation of digital nets / 13：

The decay of the Walsh coefficients of smooth functions / 14：

Arbitrarily high order of convergence of the worst-case error / 15：

Explicit constructions of point sets with best possible order of L2-discrepancy / 16：

Walsh functions / Appendix A：

Algebraic function fields / Appendix B：

References

Index

Preface

Notation

Introduction / 1：

Quasi-Monte Carlo integration, discrepancy and reproducing kernel Hilbert spaces / 2：

Geometric discrepancy / 3：

Nets and sequences / 4：

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