Is it possible to solve discrete Algebraic Riccati Equations without doing any inverse?
$$X_{k+1} = A^T X_k A -(A^T X_k B)(R + B^T X_k B)^{-1}(B^T X_k A) + Q$$ $$L =(B^T X_{k+1} B + R)^{-1}(B^TX_{k+1}A)$$
Assume that $k = 0, ... , n$
Or do I need to use LUP-factorication to solve the inverse?