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Research Article | Open Access

A greedy average block Kaczmarz method for the large scaled consistent system of linear equations

Li Wen1,2, Feng Yin1,2( ), Yimou Liao1, Guangxin Huang3
College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China
Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, Sichuan University of Science and Engineering, Zigong 643000, China
College of Mathematics and Physics, Geomathematics Key Laboratory of Sichuan, Chengdu University of Technology, Chengdu 610059, China
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Abstract

This paper presents a greedy average block Kaczmarz (GABK) method to solve the large scaled consistent system of linear equations. The GABK method introduces the strategy of extrapolation process to improve the GBK algorithm and to avoid computing the Moore-Penrose inverse of a submatrix of the coefficient matrix determined by the block index set. The GABK method is proved to converge linearly to the least-norm solution of the consistent system of linear equations. Numerical examples show that the GABK method has the best efficiency and effectiveness among all methods compared.

Keywords

block Kaczmarzextrapolated stepsizegreedy strategyGABK
CLC number: 65F10, 65F45

References

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 6792-6806
DOI: 10.3934/math.2022378

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Cite this article:
Wen L, Yin F, Liao Y, et al. A greedy average block Kaczmarz method for the large scaled consistent system of linear equations. AIMS Mathematics, 2022, 7(4): 6792-6806. https://doi.org/10.3934/math.2022378

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Received: 03 November 2021
Revised: 04 January 2022
Accepted: 10 January 2022
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)