  The orthogonal decomposition factorizes a tensor into a sum of an orthogonal
list of rankone tensors. We present several properties of orthogonal rank. We
find that a subtensor may have a larger orthogonal rank than the whole tensor
and prove the lower semicontinuity of orthogonal rank. The lower semicontinuity
guarantees the existence of low orthogonal rank approximation. To fit the
orthogonal decomposition, we propose an algorithm based on the augmented
Lagrangian method and guarantee the orthogonality by a novel orthogonalization
procedure. Numerical experiments show that the proposed method has a great
advantage over the existing methods for strongly orthogonal decompositions in
terms of the approximation error.
