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arXiv · 2602.03239

Deterministic and randomized Kaczmarz methods for $AXB=C$ with applications to color image restoration

Wenli Wang·Duo Liu·Gangrong Qu·Michiel E. Hochstenbach
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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.

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Wenli Wang, Duo Liu, Gangrong Qu, Michiel E. Hochstenbach. 2026-02-03. Deterministic and randomized Kaczmarz methods for $AXB=C$ with applications to color image restoration. https://arxiv.org/abs/2602.03239

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