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# Householder's Method

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.

Halley's Irrational Formula, Halley's Method, Newton's Method

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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. The Numerical Treatment of a Single Nonlinear Equation. New York: McGraw-Hill, 1970.Ortega, J. M. and Rheinboldt, W. C. Iterative Solution of Nonlinear Equations in Several Variables. Philadelphia, PA: SIAM, 2000.

## Referenced on Wolfram|Alpha

Householder's Method

## Cite this as:

Weisstein, Eric W. "Householder's Method." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/HouseholdersMethod.html