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Random Number Generation and Quasi-Monte Carlo MethodsRandom Number Generation and Quasi-Monte Carlo Methods

Harald Niederreiter



CBMS-NSF Regional Conference Series in Applied Mathematics 63


"The most important sections of this book deal with the fundamental concepts of nets, (t, s)-sequences, and lattice rules which are of central importance in new advances in quasi-Monte Carlo methods...It gives an excellent survey on the recent developments in uniform pseudorandom number generation and quasi-Monte Carlo methods. Some of these developments described here have never before presented in a book...Fundamental concepts and methods were explained in detail using instructive examples (e.g. numerical integration in higher dimensions, optimization,...). Hence, this publication should also be accessible for nonspecialists. For the scientific computing community it is surely a valuable contribution." -- U. Lotz, Biometric Journal, 35 (1993) 4.


Tremendous progress has taken place in the related areas of uniform pseudorandom number generation and quasi-Monte Carlo methods in the last five years. This volume contains recent important work in these two areas, and stresses the interplay between them. Some developments contained here have never before appeared in book form.

Includes the discussion of the integrated treatment of pseudorandom numbers and quasi-Monte Carlo methods; the systematic development of the theory of lattice rules and the theory of nets and (t,s)-sequences; the construction of new and better low-discrepancy point sets and sequences; Nonlinear congruential methods; the initiation of a systematic study of methods for pseudorandom vector generation; and shift-register pseudorandom numbers.

Based on a series of 10 lectures presented by the author at a CBMS-NSF Regional Conference at the University of Alaska at Fairbanks in 1990 to a selected group of researchers, this volume includes background material to make the information more accessible to nonspecialists.

Contents

Preface; Chapter 1: Monte Carlo Methods and Quasi-Monte Carlo Methods; Chapter 2: Quasi-Monte Carlo Methods for Numerical Integration; Chapter 3: Low-Discrepancy Point Sets and Sequences; Chapter 4: Nets and (t,s)-Sequences; Chapter 5: Lattice Rules for Numerical Integration; Chapter 6: Quasi- Monte Carlo Methods for Optimization; Chapter 7: Random Numbers and Pseudorandom Numbers; Chapter 8: Nonlinear Congruential Pseudorandom Numbers; Chapter 9: Shift-Register Pseudorandom Numbers; Chapter 10: Pseudorandom Vector Generation; Appendix A: Finite Fields and Linear Recurring Sequences; Appendix B: Continued Fractions; Bibliography; Index.

1992 / vi + 241 pages / Softcover / ISBN-13: 978-0-898712-95-7 / ISBN-10: 0-89871-295-5 /
List Price $76.50 / SIAM/CBMS Member Price $53.55 / Order Code CB63
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