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.