Mechanism works
2026
Numerical-Range Stabilization for Nonnormal State Dynamics
Replace spectral-radius-only stabilization of a recurrent or state-space transition matrix with a numerical-range constraint. Penalize directions in which the Hermitian part of a rotated transition matrix has a large maximal eigenvalue, controlling nonnormal transient amplification and polynomial state propagation.
Paper: Square Functions and the Complete Crouzeix Conjecture in Dimension Three
arXiv:2608.27346