A randomized block extended Kaczmarz method with hybrid partitions for solving large inconsistent linear systems

We propose a randomized block extended Kaczmarz method with hybrid partitioning techniques for solving large inconsistent linear systems. It employs the k-means clustering to partition the columns of the coefficient matrix while applying the uniform sampling to derive the row partition of the coeffi...

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Bibliographic Details
Published inApplied mathematics letters Vol. 152; p. 109027
Main Authors Jiang, Xiang-Long, Zhang, Ke
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.06.2024
Subjects
Convergence
Inconsistent linear systems
k-means clustering
Randomized extended Kaczmarz
Randomized extended Kaczmarz
k-means clustering
Inconsistent linear systems
Convergence
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Summary:We propose a randomized block extended Kaczmarz method with hybrid partitioning techniques for solving large inconsistent linear systems. It employs the k-means clustering to partition the columns of the coefficient matrix while applying the uniform sampling to derive the row partition of the coefficient matrix. It is proved that the proposed algorithm converges to the unique least-squares least-norm solution in expectation. Numerical examples validate that the new algorithm is competitive when compared with other randomized extended Kaczmarz-type methods.
ISSN:0893-9659
1873-5452
DOI:10.1016/j.aml.2024.109027