计算矩阵最大奇异值和奇异向量的交变方向幂方法

IF 1.8 3区 数学 Q1 MATHEMATICS AIMS Mathematics Pub Date : 2023-01-01 DOI:10.3934/math.2023056
Yonghong Duan, Ruiping Wen
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引用次数: 0

摘要

奇异值分解(SVD)是矩阵理论和数值线性代数中的一个重要工具。在过去的几十年里,对计算矩阵奇异值分解的有效数值算法进行了广泛的研究。本文提出了一种计算矩阵最大奇异值和奇异向量的交变方向幂法。该方法与幂函数法相似,但迭代次数较少。在适当的条件下证明了新方法的收敛性。理论分析和数值实验均表明,在某些情况下,新方法是可行的,并且比幂方法更有效。
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An alternating direction power-method for computing the largest singular value and singular vectors of a matrix
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.
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来源期刊
AIMS Mathematics
AIMS Mathematics Mathematics-General Mathematics
CiteScore
3.40
自引率
13.60%
发文量
769
审稿时长
90 days
期刊介绍: AIMS Mathematics is an international Open Access journal devoted to publishing peer-reviewed, high quality, original papers in all fields of mathematics. We publish the following article types: original research articles, reviews, editorials, letters, and conference reports.
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