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Krylov subspace methods, such as Lanczos and Arnoldi, are emerging numerical techniques for reduced-order modeling of large scale linear dynamical systems. Ths basic idea of reduced-order modeling of a dynamical system is to replace the original system by a system of the same type, but with much smaller state-space dimension. The recent surge of interest in Krylov subspace methods was triggered by the need of such techniques in the analysis and synthesis of large scale dynamic systems, such as ones in intergrated electronic circuits and structural dynamics.

In this talk, we will start with the basic ideas of reduced-order modeling techniques and then describe Krylov subspace methods and their connections with Pade approximation and other mathematical theory. Furthermore, we will discuss the stability and passivity (positive realness) of reduced-order models. Numerical examples from large scale intergrated circuits simulation will be used for demonstrating the applicability of these techniques.

Part of this work was carried out while the speaker was on sabbatical at Bell Labs. during the 1997-1998 academic year.