root of bijective function

Question

If I know that a polynomial function f(x) mapping (a, b) to (c, d) is bijective(one-one and onto), what is the fastest algorithm(On a single processor RAM machine) to find the root( f(x) = 0 ) of that function?

Answer 1

For any polynomial function of degree n>=3, i would say that the easiest way to compute the roots is the Newton's algorithm. It's probably not the fastest, but in order to make it quicker, you have to know a bit more of the functions you're going to deal with.

https://en.wikipedia.org/wiki/Newton's_method