2. Root-Finding I

Fixed-point Iteration — Quiz

Test your understanding of fixed-point iteration with 5 practice questions.

Practice Questions

Question 1

What is a fixed point of a function $g$?

Question 2

For the iteration $x_{n+1}=\frac{x_n+2}{2}$, what is the fixed point?

Question 3

If $x_0=0$ and $x_{n+1}=\cos(x_n)$, what is $x_1$?

Question 4

Which condition is commonly used to help predict local convergence of fixed-point iteration near a fixed point $p$?

Question 5

In fixed-point iteration, the original equation $f(x)=0$ is often rewritten in what form?