Image:Bairstow-fractal 6 11 m33 m33 11 6 scale 03.png

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[edit] Summary

Description

Convergence map for the en:Bairstow's method, notation following de version, similar to en:Newton fractal
Source

My own C program, derived from the newtroot program used for the newton fractals
Date

6. october 2006
Author

Lutz Lehmann User:LutzL
Permission
(Reusing this image)

my own


[edit] What it is

Bairstow's method tries to find quadratic factors of polynomials, all with real coefficients. This image shows the behaviour of different initial factors a(x)=(Z-x)^2+|y|\cdot y for x,y in the range [-3,3]. A black point indicates no convergence after ca. 100 iterations, a white point indicates a solution after one iteration, a colored point signifies convergence to the limit point located in the basin of that color. The polynomial to be factored is

f(x)=6 \cdot x^5 + 11 \cdot x^4 - 33 \cdot x^3 - 33 \cdot x^2 + 11 \cdot x + 6.

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation license".

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current13:55, 6 October 2006601×601 (41 KB)LutzL ({{Information |Description=Convergence map for the en:Bairstow's method,notation following de version, similar to en:Newton fractal |Source=My own C program, derived from the newtroot program used for the newton fractals )
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