Deterministic and randomized Kaczmarz methods for $AXB=C$ with applications to color image restoration
Numerical Analysis
2026-02-04 v1 Numerical Analysis
Abstract
We study Kaczmarz type methods to solve consistent linear matrix equations. We first present a block Kaczmarz (BK) method that employs a deterministic cyclic row selection strategy. Assuming that the associated coefficient matrix has full column or row rank, we derive matrix formulas for a cycle of this BK method. Moreover, we propose a greedy randomized block Kaczmarz (GRBK) method and further extend it to a relaxed variant (RGRBK) and a deterministic counterpart (MWRBK). We establish the convergence properties of the proposed methods. Numerical tests verify the theoretical findings, and we apply the proposed methods to color image restoration problems.
Cite
@article{arxiv.2602.03239,
title = {Deterministic and randomized Kaczmarz methods for $AXB=C$ with applications to color image restoration},
author = {Wenli Wang and Duo Liu and Gangrong Qu and Michiel E. Hochstenbach},
journal= {arXiv preprint arXiv:2602.03239},
year = {2026}
}