A root-finding algorithm based on the iteration formula
This method, like Newton's method, has poor convergence properties near any point where the derivative.
A fractal is obtained by applying Householders's method to finding a root of . Coloring the basin
of attraction (the set of initial points which converge to the same root)
for each root a different color then gives the above plots.
![x_(n+1)=x_n-(f(x_n))/(f^'(x_n)){1+(f(x_n)f^('')(x_n))/(2[f^'(x_n)]^2)}.](/images/equations/HouseholdersMethod/NumberedEquation1.svg)
.
. Coloring the basin
of attraction (the set of initial points 
which converge to the same root)
for each root a different color then gives the above plots.
