关于非负张量Z-谱半径的一些结果（英文）  

SOME RESULTS FOR Z-SPECTRAL RADIUS OF NONNEGATIVE TENSORS

作　　者：赵娜[1] 杨庆之[1] 

机构地区：[1]南开大学数学科学学院/核心数学与组合数学实验室,天津300071

出　　处：《高等学校计算数学学报》2016年第2期150-171,共22页Numerical Mathematics A Journal of Chinese Universities

基　　金：国家自然科学基金(11271206);天津市自然科学基金(12JCYBJC31200)

摘　　要：Z-eigenvalue plays a fundamental role in the best rank-one approximation.Chang,Pearson,and Zhang generalized the Perron-Probenius theorem for Z-eigenvalues of nonnegative tensors and gave some properties of the Z-spectral radius recently.In this paper,we give some properties of Z-eigenvectors associated with Z-spectral radius of nonnegative weakly symmetric tensors,compare the Zspectral radius between two nonnegative tensors,and modify the upper and lower bounds for Z-spectral radius.Some results for the Z-singular values of rectangular tensors are also given.Z-eigenvalue plays a fundamental role in the best rank-one approximation. Chang, Pearson, and Zhang generMized the Perron-Frobenius theorem for Z-eigenvalues of nonnegative tensors and gave some properties of the Z-spectral radius recently. In this paper, we give some properties of Z-eigenvectors associated with Z-spectral radius of nonnegative weakly symmetric tensors, compare the Z- spectral radius between two nonnegative tensors, and modify the upper and lower bounds for Z-spectral radius. Some results for the Z-singular values of rectangular tensors are also given.

关 键 词：nonnegative tensor IRREDUCIBLE weakly symmetric Z-spectral radius Z-singular value 

分 类 号：O22[理学—运筹学与控制论]