I have a matrix equation $\displaystyle F = X \times {D_1}{^{-1}} \times X'$, where $\displaystyle D_1$ is a diagonal invertible matrix.

Now, $\displaystyle D_1$ is updated into $\displaystyle D_2$ by $\displaystyle D_2 = D_1 + G$, where $\displaystyle G$ is a sparse diagonal matrix. Does anyone know if there is an efficiant way to update $\displaystyle F$ without having to recalculate everything?