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On a fast deterministic block Kaczmarz method for solving large-scale linear systems

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Abstract

For solving large-scale consistent systems of linear equations by iterative methods, a fast block Kaczmarz method based on a greedy criterion of the row selections is proposed. The method is deterministic and needs not compute the pseudoinverses of submatrices or solve subsystems. It is proved that the method will converge linearly to the unique least-norm solutions of the linear systems. Numerical experiments are given to illustrate that the method is more efficient and yields a significant acceleration in convergence for the tested data.

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Funding

This work was supported by NSFC under grant number 11871430.

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Authors and Affiliations

  1. School of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, Zhejiang, People’s Republic of China

    Jia-Qi Chen & Zheng-Da Huang

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  1. Jia-Qi Chen
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  2. Zheng-Da Huang
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Correspondence to Zheng-Da Huang.

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Chen, JQ., Huang, ZD. On a fast deterministic block Kaczmarz method for solving large-scale linear systems. Numer Algor 89, 1007–1029 (2022). https://doi.org/10.1007/s11075-021-01143-4

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  • DOI: https://doi.org/10.1007/s11075-021-01143-4

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