System Interpolation with Loewner Pencils: Background, Pseudospectra, and Nonlinear Eigenvalue Problems

21 May 2020
Mark Embree

In 2007, Andrew Mayo and Thanos Antoulas proposed a rational interpolation algorithm to solve a basic problem in control theory: given samples of the transfer function of a dynamical system, construct a linear time-invariant system that realizes these samples.  The resulting theory enables a wide range of data-driven modeling, and has seen diverse applications and extensions.  We will introduce these ideas from a numerical analyst's perspective, show how the selection of interpolation points can be guided by a Sylvester equation and pseudospectra of matrix pencils, and mention an application of these ideas to a contour algorithm for the nonlinear eigenvalue problem. (This talk involves collaborations with Michael Brennan (MIT), Serkan Gugercin (Virginia Tech), and Cosmin Ionita (MathWorks).)

[To be added to our seminars mailing list, or to receive a Zoom invitation for a particular seminar, please contact]

  • Computational Mathematics and Applications Seminar