Question 1
In an iterative root-finding method, what is a stopping criterion?
Question 2
If $|x_n-x_{n-1}|=0.002$ and the tolerance is $0.01$, what would a stopping rule based on successive change usually say?
Question 3
What does the residual $|f(x_n)|$ measure?
Question 4
Why is a maximum number of iterations often included in a root-finding algorithm?
Question 5
What practical problem can occur in Newton's method if $f'(x_n)=0$ or is very small?
