Publications (27)
Interpolatory Approximations of PMU Data: Dimension Reduction and Pilot Selection
Sean Reiter, Mark Embree, Serkan Gugercin +1
This work investigates the reduction of phasor measurement unit (PMU) data through low-rank matrix approximations. To reconstruct a PMU data matrix from fewer measurements, we prop…
Unstable modes in projection-based reduced-order models: How many can there be, and what do they tell you?
Mark Embree
Projection methods provide an appealing way to construct reduced-order models of large-scale linear dynamical systems: they are intuitively motivated and fairly easy to compute. Un…
Fast singular value decay for Lyapunov solutions with nonnormal coefficients
Jonathan Baker, Mark Embree, John Sabino
Lyapunov equations with low-rank right-hand sides often have solutions whose singular values decay rapidly, enabling iterative methods that produce low-rank approximate solutions.…
Analysis of GMRES for Low-Rank and Small-Norm Perturbations of the Identity Matrix
Arielle K. Carr, Eric de Sturler, Mark Embree
In many applications, linear systems arise where the coefficient matrix takes the special form , where is the identity matrix of dimension $n…
Contour Integral Methods for Nonlinear Eigenvalue Problems: A Systems Theoretic Approach
Michael C. Brennan, Mark Embree, Serkan Gugercin
Contour integral methods for nonlinear eigenvalue problems seek to compute a subset of the spectrum in a bounded region of the complex plane. We briefly survey this class of algori…
Spectral characterization of magic angles in twisted bilayer graphene
Simon Becker, Mark Embree, Jens Wittsten +1
Twisted bilayer graphene (TBG) has been experimentally observed to exhibit almost flat bands when the twisting occurs at certain magic angles. In this letter, we report new results…