How accurate is this two-pass approach in general? From my outsider's perspective, it always looked like most of the difficulty in implementing Lanczos was reorthogonalization, which will be hard to do with the two-pass algorithm.
Or is this mostly a problem when you actually want to calculate the eigenvectors themselves, and not just matrix functions?
Or is this mostly a problem when you actually want to calculate the eigenvectors themselves, and not just matrix functions?