Householder's Method

A Root-finding algorithm based on the iteration formula

$$x_{n+1}=x_n-{f(x_n)\over f'(x_n)}\left\{{1-{[f(x_n)]^2f''(x_n)\over 2[f'(x_n)]^2}}\right\}.$$

This method, like Newton's Method, has poor convergence properties near any point where the Derivative $f'(x)=0$.

See also Newton's Method

References

Householder, A. S. The Numerical Treatment of a Single Nonlinear Equation. New York: McGraw-Hill, 1970.