root-finding algorithm based on the iteration formula
This method, like
Newton's method, has poor convergence properties near any point where the derivative .
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.
See also Halley's Irrational Formula
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References Gourdon, X. and Sebah, P. "Newton's Iteration." http://numbers.computation.free.fr/Constants/Algorithms/newton.html. Householder,
A. S. New York: McGraw-Hill,
Numerical Treatment of a Single Nonlinear Equation. Ortega, J. M. and Rheinboldt, W. C. Philadelphia, PA: SIAM,
Solution of Nonlinear Equations in Several Variables. Referenced on Wolfram|Alpha Householder's Method
Cite this as:
Weisstein, Eric W. "Householder's Method."
From --A Wolfram Web Resource. MathWorld https://mathworld.wolfram.com/HouseholdersMethod.html