I am computing the pseudo-inverse of several matrices of identical size $m \times n$ . However, computation (e.g. with the LAPACK pinv) seems to be much slower in some cases (5 to 10 times slower). I observe the same effect for several values of $m \in 100 \dots 5000$, but the effect is more important with $n \approx 100$.
Is there any theoretical/empirical result which explains what can influence the computational speed of pseudo-inverse computation ? I have the suspicion that some of the matrices may be ill-conditioned. Could it be related ?
Thanks !