[Math] Using Muller’s method to find ALL roots ( real and complex) with three initial guesses.

Question

Is there any way to find all complex and real roots of a third-degree polynomial using only Muller's equation using initial guesses:

$x_0=0.6,x_1=0.7,x_2=0.8, ε_s=0.01$%

$f(x)=x^3 – x^2+3x-2 $

I have found the real root after two iterations $x_r=0.71511$

How can I find the other two complex roots without using MATLAB?

Answer 1

You can perhaps factorize the polynomial $$f(x) = (x-x_r)(x^2-(x_r+1)x + \frac{2}{x_r})$$