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arXiv · 2604.05726

On convergence of residual-based extended randomized Kaczmarz methods for matrix equations

Wendi Bao·Jing Li·Lili Xing·Weiguo Li·Jichao Wang
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Abstract

In this paper, for solving inconsistent matrix equations we propose a dual-space residual-based randomized extended Kaczmarz method and its version with Nesterov momentum. Without the full column rank assumptions on coefficient matrices, we provide a thorough convergence analysis, and derive upper bounds for the convergence rates of the new methods. A feasible range for the momentum parameters is determined. Numerical experiments demonstrate that the proposed methods are much more effective than the existing ones, especially the method with momentum.

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Wendi Bao, Jing Li, Lili Xing, Weiguo Li, Jichao Wang. 2026-04-07. On convergence of residual-based extended randomized Kaczmarz methods for matrix equations. https://arxiv.org/abs/2604.05726

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