Others have already mentioned Cramer's rule, but even if this code were switched to Gaussian elimination it might not beat lapack on big problems. Lapack implementations do extra tricks to optimize cache usage on big matrices. Would be interesting to include eigen in the benchmark too.
I've read your comment several times and can't follow it. I think you're saying that even if the author continued to use Cramer's rule, he would lose to LAPACK on big problems.
No. If he continued to use Cramer's rule, he would definitely lose to LAPACK on big problems, purely because of using Cramer's rule. But even if he didn't continue to use Cramer's rule (if he switched to Gaussian elimination), he still might lose to LAPACK, because LAPACK is pretty well optimized.
> he would definitely lose to LAPACK on big problems, purely because of using Cramer's rule.
More importantly though, the code would probably take ages (as in, "age of the universe" ages) to compile, as Cramer's rule is O(n!) (using a naive implementation, I think one could get to O(n^4) if determinant was computed using LU factorization, but what's the point of Cramer's rule then...).
