What is the most accurate way to compute $x^TA^{-1}y$ for two vectors $x$ and $y$, and a symmetric positive definite matrix $A$?
With a Cholesky decomposition $A=LL^T$, one could either apply both $L$ matrices to the same vector, i.e. $z=x^T(L^{-T}L^{-1}y)$, or split them towards the left and right, i.e. $(L^{-1}x)^T L^{-1}y$.
Do these approaches differ in their accuracy?