3.1.1 Linear Congruential Generators

$$\fbox{ $ I_{n+1} = \left[ \,a \, I_{n} + b \,\right] \, \mbox{mod} \, m $ }$$

where $a$ is some (odd) multiplicative factor, $m$ is the largest integer (hardware-dependent, e.g. $m=2^{32}$), and $b$ is relatively prime with respect to $m$.

To obtain random numbers $x_{n}$ of type real, equidistributed over the interval $(0,1)$, divide $I_{n}$ by $m$.

$\Longrightarrow$Library or internal routines RAND, RND, RAN etc.

To minimize serial correlations: