We consider the problem of solving a rational matrix equation arising in the solution of G-networks. We propose and analyze two numerical methods: a fixed point iteration and the Newton–Raphson method. The fixed point iteration is shown to be globally convergent with linear convergence rate, while the Newton method is shown to have a local convergence, with quadratic convergence rate. Numerical experiments show the effectiveness of the proposed methods.

Additional Metadata
Keywords Fixed point iteration, G-networks, Newton–Raphson method, Nonlinear matrix equation
Persistent URL dx.doi.org/10.1007/s10092-017-0214-7
Journal Calcolo
Citation
Meini, B, & Nesti, T. (2017). On the solution of a rational matrix equation arising in G-networks. Calcolo, 1–23. doi:10.1007/s10092-017-0214-7