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.
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.
Preface; 1. Monte Carlo methods and Quasi-Monte Carlo methods; 2. Quasi-Monte Carlo methods for numerical integration; 3. Low-discrepancy point sets and sequences; 4. Nets and (t,s)-sequences; 5. Lattice rules for numerical integration; 6. Quasi- Monte Carlo methods for optimization; 7. Random numbers and pseudorandom numbers; 8. Nonlinear congruential pseudorandom numbers; 9. Shift-Register pseudorandom numbers; 10. Pseudorandom vector generation; Appendix A. Finite fields and linear recurring sequences; Appendix B. Continued fractions; Bibliography; Index.
This volume contains recent work in uniform pseudorandom number generation and quasi-Monte Carlo methods, and stresses the interplay between them.
'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
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