Householder,s Method
المؤلف:
Householder, A. S
المصدر:
The Numerical Treatment of a Single Nonlinear Equation. New York: McGraw-Hill, 1970.
الجزء والصفحة:
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21-9-2021
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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.
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.
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