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

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    $\begingroup$ 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? $\endgroup$ – David Richerby Jun 27 '16 at 9:11
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    $\begingroup$ It is probably meant to "evaluate an expression". OP should clarify. $\endgroup$ – A.Schulz Jun 27 '16 at 10:53

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