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Research Article | Open Access

An alternating direction power-method for computing the largest singular value and singular vectors of a matrix

Yonghong Duan1Ruiping Wen2( )
Department of Applied Mathematics, Taiyuan University, Taiyuan 030032, Shanxi, China
Key Laboratory for Engineering and Computing Science, Shanxi Provincial Department of Education, Taiyuan Normal University, Jinzhong 030619, Shanxi, China
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Abstract

The singular value decomposition (SVD) is an important tool in matrix theory and numerical linear algebra. Research on the efficient numerical algorithms for computing the SVD of a matrix is extensive in the past decades. In this paper, we propose an alternating direction power-method for computing the largest singular value and singular vector of a matrix. The new method is similar to the well-known power method but needs fewer operations in the iterations. Convergence of the new method is proved under suitable conditions. Theoretical analysis and numerical experiments show both that the new method is feasible and is effective than the power method in some cases.

CLC number: 65F10, 65F15

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AIMS Mathematics
Pages 1127-1138

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Cite this article:
Duan Y, Wen R. An alternating direction power-method for computing the largest singular value and singular vectors of a matrix. AIMS Mathematics, 2023, 8(1): 1127-1138. https://doi.org/10.3934/math.2023056

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Received: 21 July 2022
Revised: 10 October 2022
Accepted: 11 October 2022
Published: 15 January 2023
©2023 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)