基于随机算法求解张量特征值
The Random Algorithm for Solving Eigenvalue of Tensors
DOI: 10.12677/aam.2025.149399, PDF,   
作者: 罗雨婷：广东工业大学数学与统计学院，广东 广州
关键词: 随机算法；张量；H特征值；Random Algorithm； Tensor； H-Eigenvalue
摘要: 本文围绕张量H特征值问题展开研究。文中聚焦H特征对，将张量H特征值问题转化为非线性方程组问题，并利用三种Kaczmarz算法变体(NK、NRK、NURK)进行求解，这些算法的核心差异在于迭代过程中投影行的选择策略。为验证算法有效性，通过算例进行数值实验，结果显示三种算法均能有效求解张量最大H特征值，整体验证了算法对于求解张量特征值的可行性。
Abstract: This paper focuses on the H-eigenvalue problem of tensors. In this paper, the H-eigenvalue problem of tensors is transformed into a system of nonlinear equations by focusing on the H-eigenpair, and three nonlinear Kaczmarz algorithm variants (NK, NRK, NURK) are used to solve it. The core difference between these algorithms lies in the selection strategy of projection rows during the iteration process. To verify the effectiveness of the algorithms, numerical experiments are carried out with examples. The results show that all three algorithms can effectively solve the maximum H-eigenvalue of tensors, which generally verifies the feasibility of the proposed algorithms.
文章引用：罗雨婷. 基于随机算法求解张量特征值[J]. 应用数学进展, 2025, 14(9): 60-64. https://doi.org/10.12677/aam.2025.149399

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