Is there any way to more efficiently/elegantly calculate the inverse of $I +s A$ where $A$ is a invertible matrix, $s\in\mathbb{R}$ using a known inverse $(I + s_0 A)^{-1}$?
One idea a had was using $s = s_0 + \Delta s$ which for small enough $\Delta s$ could be approximated as $$(\underbrace{I + s_0 A}_C + \underbrace{\Delta s A}_D)^{-1} \approx C^{-1} - C^{-1} D C^{-1}$$ in the sense of $D$ beeing a pertubation of $C$. But what if the $\Delta s$ is not sufficiently small, is there some way to reuse the known inverse or in general calculate/approximate the inverse of $I + s A$?
