  The computational complexity of different steps of the basic SSA is
discussed. It is shown that the use of the general-purpose "blackbox" routines
(e.g. found in packages like LAPACK) leads to huge waste of time resources
since the special Hankel structure of the trajectory matrix is not taken into
account. We outline several state-of-the-art algorithms (for example,
Lanczos-based truncated SVD) which can be modified to exploit the structure of
the trajectory matrix. The key components here are hankel matrix-vector
multiplication and hankelization operator. We show that both can be computed
efficiently by the means of Fast Fourier Transform. The use of these methods
yields the reduction of the worst-case computational complexity from O(N^3) to
O(k N log(N)), where N is series length and k is the number of eigentriples
desired.
