Suppose $B$ is $N\times N$ matrix and $A$ is $N\times M$ matrix. $A$ and $B$ is given, and Cholesky factor $L$ is also given which satisfy $B=LL^T$.
My question is how to calculate $B^{-1}A$ efficiently.
I know if $A$ was a vector, we could solve it with $O(N^2)$ by backward substitution method. Is there faster way than simply repeating backward substitution method $M$ times (this results in $O(N^2M$))?