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On multi-step greedy randomized coordinate descent method for solving large linear least-squares problems

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Abstract

To solve large-scale linear least-squares problems, we propose a multi-step greedy randomized coordinate descent method based on the greedy randomized coordinate descent method. We also prove that the new method converges to the unique solution of the linear least-squares problem when the coefficient matrix is of full rank, and the number of rows is not less than the number of columns. Finally, some numerical experiments demonstrate the effectiveness of the multi-step greedy randomized coordinate descent method in solving linear least-squares problems.

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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

We are very grateful to anonymous reviewers for their valuable comments and suggestions, which have important guiding significance to our research.

This work is partly supported by National Natural Science Foundation of China (No. 12071149), Science and Technology Commission of Shanghai Municipality (No. 20511100200, No. 22DZ2229014, 21JC1402500).

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  1. School of Mathematical Sciences, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, China

    Long-Ze Tan & Xue-Ping Guo

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  1. Long-Ze Tan
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  2. Xue-Ping Guo
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Correspondence to Xue-Ping Guo.

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Communicated by Gabriel Haeser.

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Tan, LZ., Guo, XP. On multi-step greedy randomized coordinate descent method for solving large linear least-squares problems. Comp. Appl. Math. 42, 37 (2023). https://doi.org/10.1007/s40314-022-02163-z

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  • DOI: https://doi.org/10.1007/s40314-022-02163-z

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