I have an NxN admittance Matrix, G for a purely resistive network. There are total N^2 ports in the network such that each port is connected to every other port through some admittance. As expected, G shows that port connected to its physically neighbor ports are with large admittance (small resistance) & to those far with low admittance values, i.e. admittance for the neighbor ports dominate for a given port.
I want to reduce G such that each Port is shown connected to its neighbor ports only. for e.g., in a plane a port C has two horizontal neighbor ports A, B and two vertical neighbor ports D, E and only these connections should be present.
However the admittance to ports other than neighboring ports (say those next to neighbor ports) though smaller but is still significant/comparable to make an impact.
I can not straightaway discard these entries in G but need to remodel such that the reduced G, say G_reduced is very good approximation for original G but with neighbor ports only.
Please help to know if this is feasible and how? I have tried to explore techniques like least Square fitting to find G_reduced such that it minimizes the difference between G and G_reduced but this doesn't seem to help. Not sure if eigenvalue decomposition for G could help here either?
