To make things like bridges and atoms more stable, it turns out you just need to add a little bit of random chaos into the math.
April 2, 2026
Original Paper
Stabilizing the Rayleigh--Ritz procedure by randomization
arXiv · 2604.01037
The Takeaway
The Rayleigh-Ritz procedure is a cornerstone of physics and engineering, but it is notoriously prone to crashing or giving wrong answers. Scientists solved this long-standing problem by discovering that injecting randomness into the calculation actually stabilizes it, allowing for perfect accuracy in simulating complex physical systems.
From the abstract
Extracting approximate eigenpairs from a prescribed subspace is of fundamental importance in eigenvalue computation. While projecting the target eigenvector onto the subspace yields satisfactory accuracy, extracting an approximate eigenpair that attains a comparable convergence rate has remained a long-standing open problem. Although the standard Rayleigh--Ritz procedure is widely used for this purpose, it may suffer from deteriorated convergence of Ritz values and may even fail to produce conve