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Research Article | Open Access

The k-means clustering-based CD method for solving large-scale matrix equation A X = B

Lifang Dai1, Maolin Liang1, Qun Li2( ), Ruijuan Zhao3, Yong-hong Shen4
School of Mathematics and Statistics, Tianshui Normal University, Tianshui, 741000, China
School of Data Sciences, Zhejiang University of Finance and Economics, Hangzhou, 310018, China
School of Information Engineering, Lanzhou University of Finance and Economics, Lanzhou, 730101, China
School of Mathematics and Computer Science, Northwest Minzu University, Lanzhou, 730000, China
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Abstract

In this paper, the coordinate descent (CD) method integrated with k-means clustering is proposed to address the least-squares problem of the large-scale matrix equation A X = B, where the coefficient matrix A is assumed to be of full column rank. Rigorous theoretical analysis shows that the iteration sequence generated by this method converges to the unique least-norm least-squares solution of the problem. The performed numerical results demonstrate that the method developed here is feasible and efficient.

Keywords

matrix equationleast-squaresk-means clusteringcoordinate descent method
CLC number: 15A24, 65F10

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AIMS Mathematics
Volume 11 Issue 4,
April 2026
Pages 8859-8878
DOI: 10.3934/math.2026365

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Cite this article:
Dai L, Liang M, Li Q, et al. The k-means clustering-based CD method for solving large-scale matrix equation A X = B. AIMS Mathematics, 2026, 11(4): 8859-8878. https://doi.org/10.3934/math.2026365

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Received: 06 January 2026
Revised: 07 March 2026
Accepted: 13 March 2026
Published: 01 April 2026
©2026 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)