The discretization of Maxwell equations results in a polynomial matrix equa
tion in frequency. In this paper,,ve present a robust and efficient algorit
hm for solving the polynomial matrix equation. To solve this equation for a
broad bandwidth, one previously performs a discrete frequency sweep where
the resulting matrix needs to be inverted at numerous frequencies,while cur
rent procedure requires only one matrix inversion. Speed improvements compa
red to the discrete sweep range from 10 to 100 times, depending on number o
f resonance peaks encountered.