An approximate solution for Lyapunov equations is constructed using Krylov subspaces for the purpose of order reduction. It is proved that order reduction by low rank gramians calculated in this way and used for balancing and truncation is equivalent to applying moment matching by Krylov subspace methods to the original large scale system. It is also shown that some of the Hankel singular values of the large scale system are approximated by the Hankel singular values of the reduced model. A two step order reduction is then proposed where a Krylov subspace method and truncated balanced realization (TBR) are applied, sequentially. This improves the result of Krylov subspace method while being computationally much cheaper than TBR.      «

An approximate solution for Lyapunov equations is constructed using Krylov subspaces for the purpose of order reduction. It is proved that order reduction by low rank gramians calculated in this way and used for balancing and truncation is equivalent to applying moment matching by Krylov subspace methods to the original large scale system. It is also shown that some of the Hankel singular values of the large scale system are approximated by the Hankel singular values of the reduced model. A two...     »