A derivative-free spectral residual method for computing generalized eigenpairs of weakly symmetric tensors

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Journal of Computational and Applied Mathematics Pub Date : 2025-09-23 DOI:10.1016/j.cam.2025.117088

Ruijuan Zhao , Maolin Liang , Yangyang Xu , Qun Li

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引用次数: 0

Abstract

This paper is concerned with computing generalized eigenpairs of weakly symmetric tensors. We first show that computing generalized eigenpairs of weakly symmetric tensors is equivalent to finding the nonzero solutions of a nonlinear system of equations, and then propose a derivative-free spectral residual method for it. The method utilizes the residual vector as the search direction and incorporates a derivative-free nonmonotone line search strategy, avoiding any explicit information associated with the Jacobian matrix of the considered nonlinear system of equations. Additionally, the global convergence of the method is established. Numerical results are presented to demonstrate superior efficiency of the proposed method through comparisons with the alternating least squares (ALS) method and other existing approaches. Furthermore, the results show that the proposed method can capture more, and in some cases all, generalized eigenvalues of weakly symmetric tensors.

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计算弱对称张量广义特征对的无导数谱残差法

研究了弱对称张量的广义特征对的计算问题。首先证明了计算弱对称张量的广义特征对等价于求非线性方程组的非零解，然后给出了一种无导数谱残差法。该方法利用残差向量作为搜索方向，并结合无导数的非单调线搜索策略，避免了与所考虑的非线性方程组的雅可比矩阵相关的任何显式信息。此外，还证明了该方法的全局收敛性。通过与交替最小二乘（ALS）方法和其他现有方法的比较，给出了数值结果，证明了该方法的优越性。此外，结果表明，该方法可以捕获更多的弱对称张量的广义特征值，在某些情况下可以捕获所有的广义特征值。

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来源期刊

Journal of Computational and Applied Mathematics 数学-应用数学

CiteScore

5.40

自引率

4.20%

发文量

437

审稿时长

3.0 months

期刊介绍： The Journal of Computational and Applied Mathematics publishes original papers of high scientific value in all areas of computational and applied mathematics. The main interest of the Journal is in papers that describe and analyze new computational techniques for solving scientific or engineering problems. Also the improved analysis, including the effectiveness and applicability, of existing methods and algorithms is of importance. The computational efficiency (e.g. the convergence, stability, accuracy, ...) should be proved and illustrated by nontrivial numerical examples. Papers describing only variants of existing methods, without adding significant new computational properties are not of interest. The audience consists of: applied mathematicians, numerical analysts, computational scientists and engineers.