An alternating direction power-method for computing the largest singular value and singular vectors of a matrix-Reference-Cited by-同舟云学术

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

Published:2023 Issue:1 Volume:8 Page:1127-1138
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Duan Yonghong¹,Wen Ruiping²

Affiliation:

1. Department of Applied Mathematics, Taiyuan University, Taiyuan 030032, Shanxi, China

2. Key Laboratory for Engineering and Computing Science, Shanxi Provincial Department of Education, Taiyuan Normal University, Jinzhong 030619, Shanxi, China

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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