Phase-error scaling and ranking of finite-window and partial-averaging schemes

Measure the phase-error scaling of the Koopman finite-window method at a resonance crossing and compare it with the $O(\epsilon^{4/7})$ phase-error scaling achieved by the optimally tuned partial-averaging switch, in order to rank the two schemes.

Background

The paper reports that the optimally tuned partial-averaging switch of Lynch et al. achieves a phase error of $O(\epsilon^{4/7})$. For the finite-window Koopman construction, the paper demonstrates boundedness of the generator and recovery of the leading resonant jump, but it does not quantify the corresponding phase-error scaling at a crossing.

Because the finite-window scaling has not been measured, the relative accuracy of the two approaches remains unresolved and the authors state that the schemes cannot yet be ranked.