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Description

Large scale higher order linear dynamical systems can be solved numerically using a two step process. First, we linearize the higher order system, usually with a block matrix representation of twice the dimension. Next, we apply Krylov-subspace technology (Arnoldi, Lanczos) to the larger block system. However, the Krylov subspaces induced by the equivalent first order formulations in higher dimension actually consists of multiple copies of the same underlying subspace. I have been working on an algorithm to generate an orthonormal basis of the fundamental subspace in the block matrix formulation. In this talk I will introduce some of the major players in this intellectual drama including the solution of the Quadratic Eigenvalue Problem using General Eigenvalue Problem techniques, an overview of the Arnoldi process and a discussion of the implications of this work.