We propose algorithms for Tucker approximation of 3-tensor, that use it only
through tensor-by-vector-by-vector multiplication subroutine. In matrix case,
Krylov methods are methods of choice to approximate dominant column and row
subspace of sparse or structured matrix given through matrix-by-vector
subroutine. However, direct generalization to tensor case, proposed recently by
Elden and Savas, namely minimal Krylov recursion, does not have any convergence
theory in background and in certain cases fails to compute an approximation
with desired accuracy.