Graeffe's root squaring method

[Albert Chan]

Another way to estimate location of min abs root, start with something simple.

2 + 3x = 0 --> x = -2/3, which suggested P min abs closer to -2/3 than 2/3

(2+3x)*(1+2.5*x^2) = 2 + 3x + 5x^2 + 7.5x^3 = 0 --> x = [-2/3, ±1√(-2.5)] ≈ [-0.667, ±0.632i]

7.5 ≈ 7, which suggested P min root and 2nd min root phase angle differs by about pi/2.
The 2 min roots should be far apart, in the complex plane.

Both suggestions turned out to be true, even with small degree polynomial

(11-23-2022 07:12 PM)Albert Chan Wrote:  proot(2.0 + 3x + 5x^2 + ... + 97*x^24) = 0.788∠±2.50, 0.810∠±1.03, ...

And, P with infinite degrees:

proot(2 + 3x + 5x^2 + ... + 97*x^24 + ...) = 0.807∠±2.50, 0.852∠±1.02, ...