Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 403, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cam.2021.113828
Keywords
Linear systems; Kaczmarz method; Randomized Kaczmarz method; k-means clustering; Convergence property
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In this study, a randomized block Kaczmarz method based on k-means clustering is proposed, which selects the working block submatrix using a practical probability criterion. It is proven to converge when the linear system is consistent, and a practical variant is provided. Numerical examples are used to verify the effectiveness of the methods proposed.
Following the philosophy of the block Kaczmarz methods, we propose a randomized block Kaczmarz method with the blocks determined by the k-means clustering (RBK(k)). It can be considered as an efficient variant of the relaxed greedy randomized Kaczmarz algorithm by using a practical probability criterion for selecting the working block submatrix per iteration. The new algorithm is proved to be convergent when the linear system is consistent. A practical variant of the new method is also given. Some numerical examples are given to verify the effectiveness of the proposed methods. (c) 2021 Elsevier B.V. All rights reserved.
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