高阶奇异值分解的张量双对角化方法及其应用

IF 1.8 3区数学 Q1 MATHEMATICS

Numerical Linear Algebra with Applications Pub Date : 2023-10-01 DOI:10.1002/nla.2530

A. El Hachimi, K. Jbilou, A. Ratnani, L. Reichel

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引用次数: 0

摘要

摘要在数据压缩和提取中，需要知道与三阶张量的最大奇异值相关的几个奇异三元组。本文描述了一种用t -积计算它们的新方法。给出了确定与最小奇异值相关联的一对奇异三元组的方法。提出的方法推广了现有的重新启动Lanczos双对角化方法，用于计算矩阵的几个最大或最小奇异三元组。本文的方法分别使用里兹和调和里兹横向切片来确定最大和最小奇异三联体的精确近似。计算实例显示了在数据压缩和人脸识别方面的应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A tensor bidiagonalization method for higher‐order singular value decomposition with applications

Abstract The need to know a few singular triplets associated with the largest singular values of a third‐order tensor arises in data compression and extraction. This paper describes a new method for their computation using the t‐product. Methods for determining a couple of singular triplets associated with the smallest singular values also are presented. The proposed methods generalize available restarted Lanczos bidiagonalization methods for computing a few of the largest or smallest singular triplets of a matrix. The methods of this paper use Ritz and harmonic Ritz lateral slices to determine accurate approximations of the largest and smallest singular triplets, respectively. Computed examples show applications to data compression and face recognition.

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来源期刊

Numerical Linear Algebra with Applications 数学-数学

CiteScore

3.40

自引率

2.30%

发文量

审稿时长

12 months

期刊介绍： Manuscripts submitted to Numerical Linear Algebra with Applications should include large-scale broad-interest applications in which challenging computational results are integral to the approach investigated and analysed. Manuscripts that, in the Editor’s view, do not satisfy these conditions will not be accepted for review. Numerical Linear Algebra with Applications receives submissions in areas that address developing, analysing and applying linear algebra algorithms for solving problems arising in multilinear (tensor) algebra, in statistics, such as Markov Chains, as well as in deterministic and stochastic modelling of large-scale networks, algorithm development, performance analysis or related computational aspects. Topics covered include: Standard and Generalized Conjugate Gradients, Multigrid and Other Iterative Methods; Preconditioning Methods; Direct Solution Methods; Numerical Methods for Eigenproblems; Newton-like Methods for Nonlinear Equations; Parallel and Vectorizable Algorithms in Numerical Linear Algebra; Application of Methods of Numerical Linear Algebra in Science, Engineering and Economics.