摘要
对于一般张量,本文给出二次张量特征值互补问题的二次互补特征值的一个上界,证明二次互补特征值和二次互补特征向量的个数有限.同时,本文提出计算所有二次互补特征值(若有限多个)的半正定松弛算法,并对一般张量情形,证明算法具有有限收敛性质.
In this paper, we study the quadratic tensor eigenvalue complementarity problem. We compute an upper bound for the quadratic complementarity(QC) eigenvalues for generic tensors by solving two rational polynomial problems, and we also prove that the numbers of both QC eigenvalues and QC eigenvectors are finite.A semidefinite relaxation method is proposed for computing all the QC eigenvalues, if there are finitely many ones. The method has finite convergence for generic tensors.
作者
赵瑞雪
周安娃
范金燕
Ruixue Zhao;Anwa Zhou;Jinyan Fan
出处
《中国科学：数学》
CSCD
北大核心
2022年第4期475-492,共18页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11571234,11971309和11701356)资助项目。
关键词
二次张量特征值互补问题
矩问题
Lasserre半定松弛
有限收敛性
quadratic tensor eigenvalue complementarity problem
moment problem
Lasserre semidefnite relaxation
fnite convergence
