计算张量特征对的瑞利商迭代法  

RAYLEIGH QUOTIENT ITERATION FOR COMPUTING TENSOR EIGENPAIRS

作　　者：梁浩[1] 张向韵[1] Liang Hao;Zhang Xiangyun(School of Mathematical Sciences,Shanghai Key Laboratory of PMMP,East China Normal University,Shanghai 200241)

机构地区：[1]数学科学学院,上海市核心数学与实践重点实验室,华东师范大学,上海200241

出　　处：《高等学校计算数学学报》2021年第3期292-306,共15页Numerical Mathematics A Journal of Chinese Universities

基　　金：supported by the National Key Research and Development Program of China(No.2018AAA0101001);Science and Technology Commission of Shanghai Municipality(No.20511100200);supported in part by Science and Technology Commission of Shanghai Municipality (No.18dz2271000)

摘　　要：In this paper,we propose a Rayleigh quotient iteration method(RQI)to calculate the Z-eigenpairs of the symmetric tensor,which can be viewed as a generalization of shifted symmetric higher-order power method(SS-HOPM).The convergence analysis and the fixed-point analysis of this algorithm are given.Numerical examples show that RQI needs fewer iterations than SS-HOPM while keep the amount of computation per iteration.

关 键 词：tensor eigenvalues symmetric tensor Rayleigh quotient iteration(RQI) SS-HOPM 

分 类 号：O241.6[理学—计算数学]