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In this paper, a novel technique for cascading generalized scattering matrices based on a Krylov's iterative solver is presented. This new technique is fully general, since it can be applied to solve the connection of an arbitrary number of networks, each one with an arbitrary number of ports, and it is easy to implement. This technique is able to compute, not only the modal spectra at the free ports of the global network, but also the modal spectra at the connected ports, so that the field inside the full network can be computed for an arbitrary incidence. In addition, this technique can also be used to evaluate the scattering parameters of the global network.