Lambert's Method

A Root-finding method also called Bailey's Method and Hutton's Method. If $g(x)=x^d-r$, then

$$H_g(x)={(d-1)x^d+(d+1)r\over (d+1)x^d+(d-1)r}x.$$

References

Scavo, T. R. and Thoo, J. B. ``On the Geometry of Halley's Method.'' Amer. Math. Monthly 102, 417-426, 1995.