Given a matrix $A$ and an identity matrix $E$, we can get the resultant matrix $X={(E-A)}^{-1}$. Now for a given diagonal matrix $D$, we would like to compute the matrix $Y={(E-DA)}^{-1}$. Is there any effective method for us to use the resultant matrix $X$ and $D$ to compute $Y$ ?
In short, can we compute the matrix ${(E-DA)}^{-1}$ by utilizing the result of ${(E-A)}^{-1}$ ?
Any suggestions are welcome!