ORIGINAL PAPERS

On Multi-step Greedy Kaczmarz Method for Solving Large Sparse Consistent Linear Systems

  • Long-Ze Tan ,
  • Ming-Yu Deng ,
  • Xue-Ping Guo
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  • 1. Key Laboratory of MEA (Ministry of Education) & Shanghai Key Laboratory of PMMP, School of Mathematical Sciences, East China Normal University, Shanghai, 200241, China;
    2. School of International Trade and Economics, University of International Business and Economics, Beijing, 100029, China

Received date: 2022-11-20

  Revised date: 2023-12-01

  Accepted date: 2023-12-03

  Online published: 2024-03-25

Supported by

This work is partly supported by the National Natural Science Foundation of China (No. 12071149), the Science and Technology Commission of Shanghai Municipality of China (No. 22DZ2229014), and the National Key R &D Program of China (No. 2022YFA1004403).

Abstract

Based on the greedy randomized Kaczmarz (GRK) method, we propose a multi-step greedy Kaczmarz method for solving large-scale consistent linear systems, utilizing multi-step projection techniques. Its convergence is proved when the linear system is consistent. Numerical experiments demonstrate that the proposed method is effective and more efficient than several existing classical Kaczmarz methods.

Cite this article

Long-Ze Tan , Ming-Yu Deng , Xue-Ping Guo . On Multi-step Greedy Kaczmarz Method for Solving Large Sparse Consistent Linear Systems[J]. Communications on Applied Mathematics and Computation, 2025 , 7(4) : 1580 -1597 . DOI: 10.1007/s42967-023-00358-7

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