Well, probably a hard question, but I think it's better to cry out loud :).
I noticed that
MatrixExp has a
Method option when writing this answer, which is undocumented. Since this tutorial claims that
MatrixExp uses variable-order Padé approximation, evaluating rational matrix functions using Paterson–Stockmeyer methods or Krylov subspace approximations, I guess there might exist non-
Method(s), but I can't find it out. Sadly, techniques in this post seem not to help. Does anyone know? Or is
Automatic really the only available option?