An Efficient GIPM Algorithm for Computing the Smallest V-Singular Value of the Partially Symmetric Tensor

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-26 DOI:10.1007/s10957-024-02434-1

Zhuolin Du, Chunyan Wang, Haibin Chen, Hong Yan

引用次数: 0

Abstract

Real partially symmetric tensors arise from the strong ellipticity condition problem in solid mechanics and the entanglement problem in quantum physics. In this paper, we try to compute the smallest V-singular value of partially symmetric tensors with orders (p, q). This is a unified notion in a broad sense that, when \((p,q)=(2,2)\), the V-singular value coincides with the notion of M-eigenvalue. To do that, we propose a generalized inverse power method with a shift variable to compute the smallest V-singular value and eigenvectors. Global convergence of the algorithm is established. Furthermore, it is proven that the proposed algorithm always converges to the smallest V-singular value and the associated eigenvectors. Several numerical experiments show the efficiency of the proposed algorithm.

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计算部分对称张量最小 V 星形值的高效 GIPM 算法

实局部对称张量产生于固体力学中的强椭圆性条件问题和量子物理学中的纠缠问题。本文试图计算阶数为 (p, q) 的部分对称张量的最小 V-singular 值。这是一个广义上的统一概念，即当\((p,q)=(2,2)\)时，V-singular值与M-特征值的概念重合。为此，我们提出了一种带有移位变量的广义反幂法，用于计算最小的 V-singular 值和特征向量。我们确定了算法的全局收敛性。此外，我们还证明了所提出的算法总是收敛于最小 V 正弦值和相关特征向量。几个数值实验表明了所提算法的效率。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.