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CMX Lunch Seminar

Wednesday, May 24, 2023
12:00pm to 1:00pm
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Annenberg 213
A new paradigm for computing spectra, pseudospectra, and continuous spectra of infinite-dimensional operators
Alex Townsend, Associate Professor of Mathematics, Department of Mathematics, Cornell University,

Traditional methods for solving infinite-dimensional eigenproblems usually follow the discretize-then-solve paradigm. Discretize first, and then solve the matrix eigenproblem. The discretize-then-solve paradigm can be tricky for infinite-dimensional eigenproblems as the spectrum of matrix discretizations may not converge to the spectrum of the operator. Moreover, it is impossible to fully capture the continuous part of the spectrum with a finite-sized matrix eigenproblem. In this talk, we will discuss an alternative solve-then-discretize paradigm for infinite-dimensional eigenproblems that is rigorously justified. To compute the discrete spectrum and pseudospectra, we will discuss infinite-dimensional analogues of contour-based eigensolvers and randomized linear algebra. For the continuous spectra, we will show how to calculate a smoothed version of the so-called spectral measure. I will demonstrate that our techniques avoid spectral pollution on a magnetic tight-binding model of graphene.

For more information, please contact Jolene Brink by phone at (626)395-2813 or by email at [email protected] or visit CMX Website.