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

Jonas Bresch; Oleh Melnyk

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arXiv · 2610.42071

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

Jonas Bresch·Oleh Melnyk

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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.

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Jonas Bresch, Oleh Melnyk. 2026-10-30. Stochastic Rayleigh-Ritz Ascent: Global Linear Convergence under a Spectral Gap. https://arxiv.org/abs/2610.42071

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