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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 give the bound for complexity of such algorithms?

Edit: zeros has to be real

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 give the bound for complexity of such algorithms?

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 give the bound for complexity of such algorithms?

Edit: zeros has to be real

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poeaqnwgo
poeaqnwgo
  • 81
  • 3

Root finding algorithm for an analytic function

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 give the bound for complexity of such algorithms?