Broadband model order reduction of polynomial matrix equations using single-point well-conditioned asymptotic waveform evaluation: derivations and theory

To e ect a model order reduction (MORe) process on a system which has a polynomial matrix equation dependence on the MORe parameter, researchers generally take one of two approaches. The rst is to linearize the system by introducing extra degrees of freedom and then to solve the resulting expanded, linear system with a method such as Lanczos or Arnoldi. The second approach is to work directly with the polynomial system and use a technique such as asymptotic waveform evaluation (AWE). Of course, each approach has advantages and disadvantages. In this paper, a new technique will be presented which has some desirable characteristics from both approaches and which is able to circumvent simultaneously some of their disadvantages. It can be shown that both the Arnoldi and the AWE methods are special cases of this new technique. Finally, numerical results will show the viability of the new method, which will be called the well-conditioned asymptotic waveform evaluation (WCAWE) method