  The dynamic mode decomposition (DMD) has become a leading tool for
data-driven modeling of dynamical systems, providing a regression framework for
fitting linear dynamical models to time-series measurement data. We present a
simple algorithm for computing an optimized version of the DMD for data which
may be collected at unevenly spaced sample times. By making use of the variable
projection method for nonlinear least squares problems, the algorithm is
capable of solving the underlying nonlinear optimization problem efficiently.
We explore the performance of the algorithm with some numerical examples for
synthetic and real data from dynamical systems and find that the resulting
decomposition displays less bias in the presence of noise than standard DMD
algorithms. Because of the flexibility of the algorithm, we also present some
interesting new options for DMD-based analysis.
