I know that one can compute the expression $X^{-1}\mathbf{v}$ quickly with conjugate gradient method. Is there a similar approach for computing $\mathrm{tr}(X^{-1}Y)$?
Similarly interesting to me are $\mathrm{tr}(X^{-1})$ and $\mathrm{tr}(X^{-1}YX^{-1}Y)$.
