Many important qualities of nuclear plasma confinement devices can be determined via the Poincare plot of a symplectic return map. These qualities include the locations of the magnetic core (good for nuclear fusion), and chaotic regions and magnetic islands (both typically bad for confinement). The convergence rate of ergodic averages can be used to categorize these regions, but many iterations of the return map are needed to implement this directly. Recently, it has been shown that a weighted average can be used to accelerate the convergence, resulting in a useful method for categorizing trajectories.

In this talk, we will show how a technique from sequence extrapolation, the reduced rank extrapolation method (RRE), can also be used to classify trajectories with a single linear least-squares solve. For the integrable trajectories in the core and islands, a subsequent eigenvalue problem gives the number of islands, the rotation number, and the Fourier coefficients of the invariant tori. We will show examples of this method on the standard map and a stellarator equilibrium.