I have 5 matrices $A, B, C, D$ and $E$, all of them are square matrices of the same size. I have a set of equations such that:
$$A\cdot B=C, \quad A\cdot B^2=D, \quad A\cdot B^3=E$$
For given $A, C, D$ and $E$, how can I approximate $B$? Solving for $B$ yields different matrices and I am trying to find the $B$ that gives the minimal deviation when plugged in. In a sense, I am trying to do a regression analysis but matrix-wise.