Graeffe's root squaring method

[Albert Chan]

11-23-2022, 11:10 AM

The trick does not work with all polynomial in general, only for VA ROOT P(x)
P(x) roots are all inside the unit disc., with P min abs root much smaller than 1

Let M = minimum abs root function

M(P(x)) = M(P(x)*(1-x)) = M(2 + (3-2)*x + (5-3)*x^2 + (7-5)*x^3 + ...)

We can reduce size of coefficients by 2 (or more), with 2nd order forward difference (see my next PM)

M(P(x)) = M(P(x)*(1-x)²) = M(2 + ((3-2)-2)*x + ((5-3)-(3-2))*x^2 + ((7-5)-(5-3))*x^3 + ...)