2. Root-Finding I

Convergence Concepts — Quiz

Test your understanding of convergence concepts with 5 practice questions.

Practice Questions

Question 1

In root-finding, what does it mean for a sequence of approximations $\{x_n\}$ to converge to a root $r$?

Question 2

For a fixed-point iteration $x_{n+1}=g(x_n)$, which condition is a common local test for convergence to a fixed point $p$?

Question 3

If a fixed-point iteration is started near a fixed point $p$ and $|g'(p)|>1$, what is the expected behavior?

Question 4

In the bisection method, what happens to the length of the interval after each iteration?

Question 5

If the initial bisection interval has length $b-a$, what is the interval length after $n$ iterations?