n-th Root Algorithm

What is the fastest way to calculate the n-t开发者_如何学Goh root of a number?

I'm aware of the Try and Fail method, but I need a faster algorithm.

The canonical way to do this is Newton's Method. In case you don't know, the derivative of xⁿ is nx^n-1. This will come in handy. 1 is a good first guess. You want to apply it to the function a - xⁿ

IIRC, it's superconvergent on functions of the form a - xⁿ, but either way, it's quite fast. Also, IIRC, the warning in the wiki about it failing to converge would apply to more complex functions that have properties that the 'nice' functions you are interested in lack.

Not the fastest, but it works. Substitute your chosen type:

    private static decimal NthRoot(decimal baseValue, int N)
    {
        if (N == 1)
            return baseValue;
        decimal deltaX;
        decimal x = 0.1M;
        do
        {
            deltaX = (baseValue / Pow(x, N - 1) - x) / N;
            x = x + deltaX;
        } while (Math.Abs(deltaX) > 0);
        return x;
    }

    private static decimal Pow(decimal baseValue, int N)
    {
        for (int i = 0; i < N - 1; i++)
            baseValue *= baseValue;
        return baseValue;
    }

Are you referring to the nth root algorithm ? This is not a try-and-fail method, but an iterative algorithm which is repeated until the required precision is reached.