Split-Merge: A Difference-based Approach for Dominant Eigenvalue Problem

ArXi:2501.15131v3 Announce Type: replace-cross The computation of the dominant eigenpair for symmetric positive semidefinite matrices is fundamental in numerical optimization. This work shifts the paradigm from the classical Rayleigh quotient to an unconstrained difference formulation, whose global optimum recovers the dominant eigenpair. Within this framework, we prove that gradient descent with a constant step-size $\alpha \in (0, 1)$ converges almost surely to the global optimum at a local linear rate.