TAOCP 3.2.1: The Linear Congruential Method

Section 3.2.1 exercises: 5 solved.

5 items

Section 3.2.1. The Linear Congruential Method

Exercises from TAOCP Volume 2 Section 3.2.1: 5 solved.

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Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 3.2.1: The Linear Congruential Method ›

Take, for example, $m=10$, $a=2$, $c=0$, and $X_0=1$.

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 3.2.1: The Linear Congruential Method ›

Let X_{n+1}\equiv aX_n+c \pmod m, and assume that

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 3.2.1: The Linear Congruential Method ›

**Corrected Solution for Exercise 3.

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 3.2.1: The Linear Congruential Method ›

We prove Eq.

Practice › Mathematics › TAOCP › TAOCP Vol 2: Seminumerical Algorithms › TAOCP 3.2.1: The Linear Congruential Method ›

Equation (6) states that for $k \ge 0$, X_{n+k}\equiv a^kX_n+\frac{a^k-1}{a-1}\,c \pmod m.