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In recent years, Krylov-subspace methods, such as the Lanczos process, have become widely-used tools for generating reduced-order models of large-scale time-invariant linear dynamical systems. While these techniques produce reduced-order models that are in a Pade sense optimal, in general they do not preserve possible additional properties of the system, such as passivity or reciprocity. Furthermore, in the case of higher-order systems, standard Krylov-subspace methods need to be applied to an equivalent first-order formulation of the higher-order system, and as a result, the reduced-order models do not preserve the higher-order structure of the original system. In this talk, we describe suitable variants of Krylov-subspace methods that preserve these additional properties and structures of the original system. While the resulting reduced-order models are no longer optimal in a Pade sense, we show that they still satisfy a Pade-type approximation property. Numerical results for a variety of examples from VLSI circuit simulation are presented.. You can view Dr. Freund's home page at: http://cm.bell-labs.com/who/freund/