一种求解对称张量Z-特征值的非单调拟牛顿算法
A Non-Monotone Quasi-Newton Algorithm for Computing Z-Eigenvalues of Symmetric Tensors
段复建 1张义 1李向利1
作者信息
- 1. 桂林电子科技大学数学与计算科学学院,广西桂林 541004
- 折叠
摘要
张量特征值问题是近几年热门的研究问题,其中对称张量Z-特征值在数理统计、信号处理等方面有重要应用.根据对称张量Z-特征值问题与非线性方程组的等价转化,利用非单调线搜索,提出一种求解对称张量Z-特征值的拟牛顿算法.该算法不需要计算和储存雅可比矩阵,提高了计算效率.在适当的条件下,证明了算法的全局收敛性,数值实验表明,算法是可行有效的.
Abstract
The tensor eigenvalues problem has attracted people's attention in recent years,which has important applications in mathematical statistics and signal processing especially Z-eigenvalues of symmetric tensor.According to the equivalence transformation between Z-eigenvalues of symmetric tensor and nonlinear equations.Using the non-monotone line search,a convergent Quasi-Newton algorithm is proposed for computing Z-eigenvalues of a symmetric tensor.The algorithm does not require the calculation and storage of Jacobian matrices,which can improve the efficiency of computing.During the iteration process,the positive determinism of the Quasi-Newton matrix is guaranteed.Under appropriate conditions,global convergence of the proposed algorithm is established.Numerical experiments are listed to illustrate the efficiency of the proposed method.
关键词
对称张量/Z-特征值/非线性方程组/拟牛顿方法Key words
symmetric tensors/Z-eigenvalues/nonlinear equations/Quasi-Newton method引用本文复制引用
出版年
2024
NETL
NSTL
万方数据