Summary

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 ${\displaystyle a(x)=(Z-x)^{2}+|y|\cdot y}$ 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

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

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