All Questions

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 work of Friedman and Ko, page 342, Corollary 4.3.1 states that all zeros of analytic polynomial time computable function are polynomial time computable, but for me that is not clear how it could ...

Is there a method to find the value of the $n$-th decimal place of $\pi$ which is more efficient than having to compute all decimal places before as well?

As a result of some inductive procedure for each $n$ I have a system of about $n^2$ polynomial equations with $n$ variables with integer coefficients, which can be precisely computed. As the system is ...

Sorry if this is too simple. This is my first question here. Suppose $f : R^n \to R$ is a differentiable function. Say that we can compute in $T$ arithmetic operations the value $f(x)$ at any point $...

Short version of the question: Presumably, it's poly$(t)$. But what polynomial, and could you provide a reference? Long version of the question: I'm sort of surprised to be asking this, because ...