A second-order method on the Stiefel manifold via Newton$\unicode{x2013}$Schulz

ArXi:2605.02838v1 Announce Type: cross Retraction-free approaches offer attractive low-cost alternatives to Riemannian methods on the Stiefel manifold, but they are often first-order, which may limit the efficiency under high-accuracy requirements. To this end, we propose a second-order method landing on the Stiefel manifold without invoking retractions, which is proved to enjoy local quadratic (or superlinear for its inexact variant) convergence.