摘要
基于计算非负张量谱半径的高阶幂法,给出一种新的迭代算法判定强H-张量.结合不等式的放缩技巧和非负张量的Perron-Frobenius定理证明所给算法在有限步内停止,且其收敛速度是线性收敛的.数值算例表明,该算法能判定任意给定的张量是否为强H-张量,且在某些情形下比经典的强H-张量判定算法所需迭代步数更少.
Based on the higher-order power method for computing the spectral radius of nonnegative tensors,we proposed a new iterative algorithm for determining strong H-tensors.We proved that the given algorithm stopped in a finite step and its convergence rate was linear convergence by combined with the scaling technique of inequality and Perron-Frobenius theorem of nonnegative tensors.Some numerical examples show that the algorithm can determine whether a given tensor is a strong H-tensor or not.The iterative steps of the algorithm are less than that of the classical algorithm for determining strong H-tensors in some cases.
作者
刘蕊
刘奇龙
陈震
LIU Rui;LIU Qilong;CHEN Zhen(College of Mathematical Sciences, Guizhou Normal University, Guiyang 550025, China)
出处
《吉林大学学报(理学版)》
CAS
北大核心
2019年第5期1081-1087,共7页
Journal of Jilin University:Science Edition
基金
国家自然科学基金(批准号:11671105)
贵州省教育厅自然科学研究项目(批准号:黔教合KY字[2015]352号)
贵州师范大学2017年博士科研启动项目(批准号:GZNUD[2017]26号)
关键词
强H-张量
迭代算法
线性收敛
strong H-tensor
iterative algorithm
linear convergence