I have a 3-dimensional array that is potentially very large and I need to do quite a lot of operations with it.
Is there a systematic way to choose a subspace of a certain size, such that the norm (any norm) of the projection of the array onto the subspace is as large as possible?
If it was two dimensions I would diagonalize and then then add eigenvectors to my subspace with the largest eigenvalue until I was satisfied. But what do you do with 3-dimensional array?
Btw, I'm a physicist and the 3-dimensional array is the electron-phonon coupling:)