4
$\begingroup$

What is that fastest algorithm that can calculate a lot of digits of a decimal root? For example: 10,000 digits of the 3.56th root of 60.1?

$\endgroup$
  • $\begingroup$ I don't know the algorithm... but this package might help. $\endgroup$ – WhatsUp Aug 2 '15 at 14:07
  • 1
    $\begingroup$ What did you try? $\endgroup$ – Sagnik Aug 2 '15 at 14:08
  • $\begingroup$ Another optimized package for arbitrary precision. $\endgroup$ – rcgldr Oct 3 '15 at 4:15
1
$\begingroup$

An iterative method may be as follows:

$x_2=\frac{x_1(n-1)+\frac{x}{x_1^{n-1}}}{n}$

where $n$ is the root desired, $x_1$ is a guess of the root of $x$ and $x_2$ is a better guess.

The iterative method is given in the book The Art of Programming Embedded Systems by Jack G. Ganssle.

$\endgroup$
  • $\begingroup$ Perhaps "The normal procedure" could be fixed. ​ $\endgroup$ – user12859 Aug 2 '15 at 17:13
  • $\begingroup$ Sorry. Didn't notice at all. $\endgroup$ – Sagnik Aug 2 '15 at 18:01
  • $\begingroup$ Uh, I just meant replacing $ylnx$ with $(\ln(x))/y$. $\;$ $\endgroup$ – user12859 Aug 2 '15 at 18:18
  • $\begingroup$ Wouldn't that method have a problem with $n = 1 \pm \epsilon_{mach}$? $\endgroup$ – Francesco Gramano Aug 14 '15 at 23:55
  • $\begingroup$ That is Newton's method. $\endgroup$ – vonbrand Sep 1 '15 at 20:13

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.