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

doi:10.1007/s42967-023-00358-7

Abstract

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.

Key words: System of linear equations, Kaczmarz method, Greedy randomized Kaczmarz (GRK) method, Multi-step greedy Kaczmarz method, Convergence

CLC Number:

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.

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