# Computing $\mathrm{tr}(X^{-1}Y)$ efficiently

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 $\mathrm{tr}(X^{-1}YX^{-1}Y)$.

• I'm confused. None of the "equations" you're trying to solve is an equation: they're all expressions. Also, what did you try? Where did you get stuck? – David Richerby Jun 27 '16 at 9:11
• It is probably meant to "evaluate an expression". OP should clarify. – A.Schulz Jun 27 '16 at 10:53