Monday, July 14

10:30 AM-12:30 PM
Kresge Auditorium

MS1
Non-Normal Matrix Eigenvalue Problems (Part I of II)

Non-normal matrix eigenvalue problems arise in a variety of physical and engineering applications, most prominently in stability analyses: of electrical networks; of flutter phenomena in aeronautics; of ordinary differential equations; of numerical methods for the solution of partial differential equations; and of Markov chains. Non-normal eigenvalue problems are more difficult to solve than normal (e.g. symmetric, Hermitian) problems because eigenvalues and invariant subspaces can be highly sensitive to changes in the matrix. Part I of the minisymposium deals with perturbation theory, in particular with reliable indicators for measuring the sensitivity of eigen information. Part II examines how non-normality affects the behavior of numerical methods for solving eigenvalue problems.

Organizer: Ilse C. F. Ipsen
North Carolina State University

10:30 Spectral Condition Numbers for Non-Normal Matrices

James V. Burke, University of Washington; Julio Moro, Universidad Carlos III, Spain; and Michael L. Overton, Courant Institute of Mathematical Sciences, New York University

11:00 Sensitivity of Eigenvalues

Ilse C. F. Ipsen, Organizer

11:30 Non-Normality and Card Shuffling -- the "Cutoff Phenomenon" in Markov Chains

Lloyd N. Trefethen, Cornell University

12:00 Title and speaker to be announced

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