梯度神经网络方法求解含有绝对值形式张量特征值
Gradient Neural Network Method for Solving Tensor Eigenvalues with Absolute Value Form
DOI: 10.12677/aam.2024.139423, PDF,   
作者: 蔡泽福：云南师范大学数学学院，云南 昆明
关键词: 张量；特征值；梯度神经网络；Tensor； Eigenvalue； Gradient Neural Network
摘要: 目前，关于特征值的研究主要集中在特征值互补、特征值估计和运用算法计算特征值等方向。受张量绝对值方程 A x m−1 −| x |=b 启示，本文考虑一类新形式的特征值问题，并提出梯度神经网络方法求解新形式张量特征值和特征向量。数值实验表明了梯度神经网络方法求解该问题的可行性和有效性。
Abstract: At present, research on eigenvalues mainly focuses on complementary eigenvalues, eigenvalue estimation, and the application of algorithms to calculate eigenvalues. Inspired by the tensor absolute value equation A x m−1 −| x |=b , this paper considers a new form of eigenvalue problem and proposes a gradient neural network method to solve the eigenvalues and eigenvectors of the new form tensor. Numerical experiments have shown the feasibility and effectiveness of using gradient neural network methods to solve this problem.
文章引用：蔡泽福. 梯度神经网络方法求解含有绝对值形式张量特征值[J]. 应用数学进展, 2024, 13(9): 4442-4448. https://doi.org/10.12677/aam.2024.139423

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