Stochastic Rayleigh-Ritz Ascent: Global Linear Convergence under a Spectral Gap

arXiv cs.NA2026-11-02 13:000 views

arXiv:2610.42071v1 Announce Type: cross Abstract: We consider the adjoint-free random-plane iteration algorithm for finding the top eigenvector of a matrix proposed in (SIAM J. Matrix Anal. Appl. 47 (2026), 1349-1374). Unlike standard methods such as the power method or gradient descent, the above algorithm lacked linear convergence guarantees in the presence of a spectral gap. In this paper, we establish explicit spectral-gap-dependent global linear convergence rates in expectation, providing quantitative guarantees for the empirically observed convergence.

Source：https://arxiv.org/abs/2610.42071

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