Randomized block Kaczmarz methods with k-means clustering for solving large linear systems
Jiang, Xiang-Long 1Zhang, Ke 1Yin, Jun-Feng2
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作者信息
1. Shanghai Maritime Univ
2. Tongji Univ
折叠
Abstract
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.
Key words
Linear systems/Kaczmarz method/Randomized Kaczmarz method/k-means clustering/Convergence property/ALGEBRAIC RECONSTRUCTION TECHNIQUES/ALGORITHM
NSTL
Elsevier