130 citations · 345 across the 38 of their papers we have counts for
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The Multiverse of Dynamic Mode Decomposition Algorithms
Matthew J. Colbrook
Dynamic Mode Decomposition (DMD) is a popular data-driven analysis technique used to decompose complex, nonlinear systems into a set of modes, revealing underlying patterns and dyn…
Beyond expectations: Residual Dynamic Mode Decomposition and Variance for Stochastic Dynamical Systems
Matthew J. Colbrook, Qin Li, Ryan V. Raut +1
Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectra…
Avoiding discretization issues for nonlinear eigenvalue problems
Matthew J. Colbrook, Alex Townsend
The first step when solving an infinite-dimensional eigenvalue problem is often to discretize it. We show that one must be extremely careful when discretizing nonlinear eigenvalue…
Restarts subject to approximate sharpness: A parameter-free and optimal scheme for first-order methods
Ben Adcock, Matthew J. Colbrook, Maksym Neyra-Nesterenko
Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of fi…