Random Number Generation and Quasi-Monte Carlo MethodsTremendous 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. |
Contents
CB63_ch1 | 1 |
CB63_ch2 | 13 |
CB63_ch3 | 23 |
CB63_ch4 | 47 |
CB63_ch5 | 101 |
CB63_ch6 | 147 |
CB63_ch7 | 161 |
CB63_ch8 | 177 |
CB63_ch9 | 191 |
CB63_ch10 | 205 |
CB63_appendixa | 217 |
CB63_appendixb | 219 |
CB63_backmatter | 223 |
Other editions - View all
Random Number Generation and Quasi-Monte Carlo Methods Harald Niederreiter No preview available - 1992 |
Random Number Generation and Quasi-Monte Carlo Methods Harald Niederreiter No preview available - 1992 |
Common terms and phrases
algorithm characteristic polynomial Comp computational consider construction continued fraction defined Definition deg(h digits distribution DN(P elementary interval elements error bound exists figure of merit finite field follows formula Fq[x function h₁ Halton sequence hence ϳ implied constant depends inequality integer interval in base inversive congruential irreducible polynomials lattice points lattice structure lattice test Lemma linear congruential method linear congruential PRN linear recurring sequence low-discrepancy point sets low-discrepancy sequences lower bound Math matrix mod f modulo Monte Carlo method N₁ Niederreiter node set nonzero h numerical integration obtain optimization order of magnitude Pa(g per(yn point set consisting polynomial ƒ polynomial over F prime power primitive polynomial proof of Theorem pseudorandom numbers quasi-Monte Carlo methods quasirandom random numbers recursion result s)-net in base satisfies serial test star discrepancy statistical theory upper bound vectors yields Σ Σ