All solutions to Quadratic matrix polynomials I am after two things:
1- algorithms for finding all solutions of possibly large quadratic matrix equations of the form $AX^2+BX+C=0$
2- (if possible) software implementing the algorithms
Everything except Grobner basis based methods.
Thanks,
Pat

Normally, $X$ is a vector. So, $X^2$ does not make sense much.
I hack your question a bit. 
$$A^T X + X A - X B R^{-1} B^T X + Q = 0$$
It is called Algebraic Riccati Equation.
What software for solving it?
C++ or MATLAB
