Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

An Arnoldi Type Algorithm for Higher Order Linear Dynamical Systems

Student-Run Applied & Math Seminar

Speaker: Jeffrey Anderson, UC Davis
Location: 2112 MSB
Start time: Wed, Oct 20 2010, 12:00PM

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.