  We consider three different ways of algorithmization of the
Janashia-Lagvilava spectral factorization method. The first algorithm is faster
than the second one, however, it is only suitable for matrices of low
dimension. The second algorithm, on the other hand, can be applied to matrices
of substantially larger dimension. The third algorithm is a superfast
implementation of the method, but only works in the polynomial case under the
additional restriction that the zeros of the determinant are not too close to
the boundary. All three algorithms fully utilize the advantage of the method
which carries out spectral factorization of leading principal submatrices
step-by-step. The corresponding results of numerical simulations are reported
in order to describe the characteristic features of each algorithm and compare
them to other existing algorithms.
