2. Numerical Methods

Root Finding — Quiz

Test your understanding of root finding with 5 practice questions.

Practice Questions

Question 1

Which hybrid root-finding method combines the reliability of the Bisection Method with the speed of Secant and inverse quadratic interpolation to achieve robust and fast convergence?

Question 2

For the function $f(x)=x^3-2x-5$, apply one iteration of Newton's Method starting from $x_0=2$ to compute $x_1$. What is the value of $x_1$?

Question 3

How many iterations of the Bisection Method are required to reduce the interval $[3,7]$ to a length of at most $10^{-3}$?

Question 4

In fixed-point iteration $x_{n+1}=g(x_n)$ for finding a root in $[a,b]$, besides requiring $|g'(r)|<1$ at the fixed point $r$, what global condition on $g$ ensures convergence for any initial $x_0\in[a,b]$?

Question 5

What is the primary purpose of step size damping (line search) in Newton's Method implementations?