I have a matrix equation that looks like:
\begin{equation} O = RIA \end{equation}
Where my matrices have the following properties:
- $R$: Lower triangular and Toeplitz matrix. Max size about $600 \times 600$.
- $A$: Toeplitz sparse and symmetric matrix with 4 entries per column. Max size about $40 \times 40$.
I need to solve (for an arbitrary Output matrix $O$, max size $600 \times 40$), the corresponding $I$.
I guess that in the worst case I could compute it as
\begin{equation} I = R^{-1}OA^{-1} \end{equation}
but I was wondering if there are faster ways to solve this given the properties of my matrices. I haven't been able to find resources online for my use case, I would appreciate if people can point me in the right direction.