Numerical Analysis and Scientific Computing Seminar

Contour Integral Methods for Nonlinear Eigenvalue Problems: A System Theoretic Approach

Speaker: Mark Embree, Virginia Tech

Location: Warren Weaver Hall 1302

Date: Dec. 6, 2019, 10 a.m.


Nonlinear matrix eigenvalue problems exhibit fascinating structure: for example, finite dimensional problems can have infinitely many eigenvalues.  Lacking a settled, general-purpose method for solving such problems, the field is at a dynamic stage of algorithmic innovation.   A class of methods based on complex contour integration has shown great promise.  We will introduce this class of methods, establishing a connection to system realization algorithms in control theory.  This link motivates a new algorithm for the nonlinear eigenvalue problem based on rational interpolation.  This technique draws heavily upon the Loewner matrix tools developed by Mayo and Antoulas for data-driven system realization and model reduction.
Joint work with Michael Brennan and Serkan Gugercin