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 trigged by the need of such techniques in the simulation of extreme large dynamic systems, such as the ones in intergrated electronic circuits and structure analysis.

In this talk, we will start with the basic ideas of reduced-order modeling techniques based on Krylov subspaces and then describe theoretical background associated with Pade and partial Pade approximations. Numerical examples from large scale intergrated circuits simulation will be used for demonstating the applicability of these techniques.