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Niederreiter H. — Random number generation and quasi-Monte Carlo methods
Niederreiter H. — Random number generation and quasi-Monte Carlo methods

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Название: Random number generation and quasi-Monte Carlo methods

Автор: Niederreiter H.

Аннотация:

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.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 250

Добавлена в каталог: 13.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adaptive methods      152
Antithetic variates      8 107
Basis test      173
Bounded metric space      148
Cartesian product of integration rule      1
Cartesian product of trapezoidal rule      2
Central limit theorem      5
Characteristic polynomial      218
Completely uniformly distributed      162
Composition method      165
Congruential generator      177
Convergent      219 220
Copy rule      144
Crude search      150
Curse of dimensionality      2
Determinant of lattice      131
Diaphony      22
Digital multistep method      192
Digital multistep pseudorandom numbers      192
Discrepancy      13 21
Discrepancy, discrete      215
Discrepancy, extreme      14
Discrepancy, isotropic      17 21
Discrepancy, star      14
Discrete discrepancy      215
Discretization error      42
dispersion      148
Dual basis      218
Dual lattice      126
Elementary interval      48
Extreme discrepancy      14
Fibonacci numbers      122
Figure of merit      108 133 171 193 200 209
First-order congruential method      177
First-order nonlinear method      213
Formal Laurent series      88 98
Fractional part      26 28
Frequency test      166 168
Gap test      166
Generalized feedback shift-register (GFSR) method      198
Generalized feedback shift-register (GFSR) pseudorandom numbers      199
Generalized Halton sequence      45
Generalized Hammersley point set      45
Generalized van der Corput sequence      25
Generator matrix      131
Good lattice point      109 158
grid      173
Halton sequence      29 44 45 157 159
Hammersley point set      31 44 45 157 158
Hermite normal form      132
Integration lattice      126
Invariants      131
Inversion method      164
Inversive congruential generator      182 187
Inversive congruential method      182
Inversive congruential pseudorandom numbers      182 187
Inversive method      214
Irregularities of distribution      24 33 154
Isotropic discrepancy      17 21
Koksma — Hlawka inequality      19
Koksma’s inequality      18 21
Kolmogorov complexity      163
Kolmogorov test      166
Kolmogorov — Smirnov law      166
Latin square      60
Lattice      126
Lattice basis      131
Lattice methods      101
Lattice rule      101 126
Lattice structure      172 208
Lattice test, $s$-dimensional      178
Lattice tests      173
Law of the iterated logarithm      166 168
Linear congruential method      168
Linear congruential pseudorandom numbers      169
Linear recurring sequence      218
Localization of search      151
Low-discrepancy point set      23
Low-discrepancy sequence      23
Matrix generator      206
Matrix method      205
Maximal period sequence      218
Maximum metric      150
Method of good lattice points      101
Minimal polynomial      218
Mixed congruential method      169
Modulus of continuity      18 20 148
Monte Carlo estimate      4-6
Monte Carlo method      2 3
Multiple recursive method      174
Multiple-recursive pseudorandom numbers      174
Multiplicative congruential method      169
Multiplier      169
Mutually orthogonal      60
Mutually orthogonal squares      60
Net      47 48
Node set      126
Nonlinear congruential generator      178
Nonlinear congruential methods      178
Nonlinear congruential pseudorandom numbers      178
Nonuniform pseudorandom numbers      164
Nonuniform random numbers      162
Nonuniformity      22
Normal numbers      163
Orthogonal Latin squares      60-62
Outer iteration      152
Partial quotients      219 220
Periodic      164
Periodization      107
Permutation polynomial      178
Permutation test      167
Physical random numbers      163
Point set      14
Point set, generalized Hammersley      45
Point set, Hammersley      31 44 45 157 158
Point set, low-discrepancy      23
Primitive polynomial      217
Projection regular      132
Pseudorandom numbers      3 164-168
Pseudorandom vectors      3 205-208
Quadratic congruential method      181
Quadratic congruential pseudorandom numbers      181
Quasi — Monte Carlo approximation      10
Quasi — Monte Carlo method      3 9
Quasirandom points      23
Quasirandom search      148
Quasirandom sequences      23
Radical-inverse function      24
random number generation      3 161
Random search      147 158
Random variates      162
Random vector generation      3 205
Rank      131
Ratio-of-uniforms method      165
Rejection method      165
Run test      166
SEQUENCE      14
Sequence, $(t, s)-$      47 48
Sequence, completely uniformly distributed      162
Sequence, generalized Halton      45
Sequence, generalized van der Corput      25
Sequence, Halton      29 44 45 157 159
Sequence, linear recurring      218
Sequence, low-discrepancy      23
Sequence, maximal period      218
Sequence, periodic      164
Sequence, quasirandom      23
Sequence, uniformly distributed      13
Sequence, Van der Corput      25 44 45 74 92
Serial correlation      167
Serial correlation coefficient      167
Serial test      167 208
Shift-register pseudorandom numbers      191
Simulation methods      6
Spectral test      168
Standard deviation      5
Star discrepancy      14
Statistical tests for randomness      166
Stochastic simulation      6
Stratified sampling      7 144
Strong Law of Large Numbers      4
Totally bounded      149
Trace      217
Trapezoidal rule      1
Uniform pseudorandom numbers      164
Uniform pseudorandom vectors      205
Uniform random numbers      162
Uniformity test      166
Uniformly distributed      13
Van der Corput sequence      25 44 45 74 92
Variance      4
Variance reduction      7
Variation      19 22
Zaremba’s conjecture      123
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