QuadraticMatrixEquation

Solve

$AX² + BX + C = 0$

and

$X²A + XB + C = 0$

where $A$, $B$ and $C$ are $n \times n$ complex matrices.

using Newton-Raphson.

Observation: The Sylvester equation to find the Fréchet derivative is evaluated using the MatrixEquations package (https://github.com/andreasvarga/MatrixEquations.jl) and the documentation (https://docs.juliahub.com/MatrixEquations/1uOBF/2.4.2/sylvester.html)