my lecture note states that the bisection and newton method for finding roots are most of the time complementary to each other but I can not figure out why. I have basic understanding of both of the methods but I don't see them as being complementary to each other. Can anyone please explain this to me.
Thank you very much
To complete what André Nicolas said:
The bisection is slower (it converges linearly) but it converges globally (which means any starting point works).
On the other hand, Newton is quick (it converges quadratically in most cases), but does not converge globally, a bad starting point will not find the wanted solution.