PreprintCC BY 4.0arXiv
Stochastic Rayleigh-Ritz Ascent: Global Linear Convergence under a Spectral Gap
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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BibTeX
@misc{bresch2026stochastic,
title = {{Stochastic Rayleigh-Ritz Ascent: Global Linear Convergence under a Spectral Gap}},
author = {Jonas Bresch and Oleh Melnyk},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.42071},
eprint = {2610.42071},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.42071},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stochastic Rayleigh-Ritz Ascent: Global Linear Convergence under a Spectral Gap
AU - Jonas Bresch
AU - Oleh Melnyk
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.42071
UR - https://arxiv.org/abs/2610.42071
AB - 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.
ER -