Exercise 1.8 · 习题

Exercise 1.8: Newton’s method for cube roots is
based on the fact that if y is an approximation to the cube root of x,
then a better approximation is given by the value

x

/

y
2

+
2
y

3

.

Use this formula to implement a cube-root procedure analogous to the

square-root procedure. (In 1.3.4 we will see how to implement

Newton’s method in general as an abstraction of these square-root and cube-root

procedures.)

练习 1.8：牛顿法求立方根基于如下事实：若 y 是 x 的立方根的近似值，则更好的近似值由

(x/y² + 2y) / 3

给出。利用这个公式，实现一个类似于平方根过程的立方根过程。（在 1.3.4 节中，我们将看到如何将牛顿法作为这些平方根和立方根过程的抽象，以通用的方式实现。）