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

作　　者：段复建[1] 张义 李向利[1] DUAN Fu-jian;ZHANG Yi;LI Xiang-li(School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《数学的实践与认识》2024年第8期206-215,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11961010)。

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.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 Zeigenvalues 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 

分 类 号：O241.6[理学—计算数学]