UWEE Tech Report Series

Model Order Reduction by Dominant Subspace Projection: Error Bound, Subspace Computation and Circuit Applications


Guoyong Shi and C.-J. Richard Shi

Circuit simulation, dominant subspace, error bound, Krylov subspace, model order reduction, moment matching.


Balanced truncation is a well-known technique for model order reduction with a known uniform reduction error bound. Its practical use is, however, limited to small-size problems due to its cubic computation complexity. While model order reduction by projection to approximate dominant subspace without balancing has yielded encouraging experimental results, its error bound has not been analyzed. Starting from a frequency-domain solution of the Lyapunov equation, this paper first derives a square-integral reduction error bound for non-balanced dominant subspace projection, which is valid in both the frequency and time domains. Then the computation of approximate dominant subspace via three Krylov subspaces is studied. It is justified analytically that the Krylov subspace by moment matching at low frequency gives rise to a better approximation of dominant subspace than that by moment matching at high frequency. Moreover, upon establishing a new connection between a rational Krylov subspace and waveform matching in the discrete time domain, we point out that it is possible to use a rational Krylov subspace for an even better approximation by choosing an appropriate parameter. The algorithms for approximate dominant subspace computation and their applications to model order reduction are tested by using several circuit examples.

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