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arXiv · 2606.06057

Residual-based Kaczmarz methods for tensor linear equations with t-product

Li-Lin Ji·Juanjuan Sun·Jun-Feng Yin
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Abstract

Tensor linear systems widely arise from high-dimensional data mining and computing, for instance, natural language processing and machine learning. A class of residual-based tensor Kaczmarz method is proposed for tensor linear equations with t-product. Theoretical analyses prove the convergence and give an upper bound of the convergence rate of the proposed method. Furthermore, an accelerated residual-based Kaczmarz method with heavy ball momentum is developed. Numerical experiments verify the efficiency of the proposed methods and demonstrate that they are faster than the existing tensor Kaczmarz methods.

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Li-Lin Ji, Juanjuan Sun, Jun-Feng Yin. 2026-06-04. Residual-based Kaczmarz methods for tensor linear equations with t-product. https://arxiv.org/abs/2606.06057

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