Given an analytic function $f(x)$. What is the best algorithm to find roots on the interval $[a,b]$ inside the radius of convergence> What is its complexity with respect to the length of input of the interval (i. e. length of numbers $a$ and $b$)? Does [the work, section 4](https://core.ac.uk/download/pdf/81983170.pdf) give the bound for complexity of such algorithms?

Edit: zeros has to be real