张量E-特征值包含集及其应用
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摘要
针对张量E-特征值定位问题,利用不等式放缩技巧,给出E-特征值包含集,推广并改进某些已有结果.作为应用,给出弱对称非负张量Z-谱半径的更精确上界.
For locations of E-eigenvalues of tensors,some E-eigenvalue inclusion sets for tensors are obtained by using techniques of inequalities. The result generalizes and improves some known existing results. As an application,a more accurate upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained.
For locations of E-eigenvalues of tensors,some E-eigenvalue inclusion sets for tensors are obtained by using techniques of inequalities. The result generalizes and improves some known existing results. As an application,a more accurate upper bound for the Z-spectral radius of weakly symmetric nonnegative tensors is obtained.
引文
[1]CHANG K C,PEARSON K,ZHANG T. Some variational principles for Z-eigenvalues of nonnegative tensors[J]. Linear Algebra Appl,2013,438(11):4166-4182.
[2]QI L Q. Eigenvalues of a real supersymmetric tensor[J]. J Symb Comput,2005,40(6):1302-1324.
[3]LIM L H. Singular values and eigenvalues of tensors:a variational approach[C]//IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing. Puerto Vallarta,Mexico:IEEE,2005:129-132.
[4]ZHANG T,GOLUB G H. Rank-one approximation to higher order tensors[J]. SIAM J Matrix Anal Appl,2001,23(2):534-550.
[5]SONG Y S,QI L Q. Spectral properties of positively homogeneous operators induced by higher order tensors[J]. SIAM J Matrix Anal Appl,2013,34(4):1581-1595.
[6]LI W,LIU D D,VONG S W. Z-eigenpair bounds for an irreducible nonnegative tensor[J]. Linear Algebra Appl,2015,483:182-199.
[7]HE J. Bounds for the largest eigenvalue of nonnegative tensors[J]. J Comput Anal Appl,2016,20(7):1290-1301.
[8]HE J,LIU Y M,KE H,et al. Bounds for the Z-spectral radius of nonnegative tensors[J]. Springer Plus,2016,5(1):1727.
[9]LIU Q L,LI Y T. Bounds for the Z-eigenpair of general nonnegative tensors[J]. Open Math,2016,14(1):181-194.
[10]WANG G,ZHOU G L,CACCETTA L. Z-eigenvalue inclusion theorems for tensors[J]. Discrete Contin Dyn Syst,2017,B22(1):187-198.
[11]ZHAO J X,SANG C L. Two new eigenvalue localization sets for tensors and theirs applications[J]. Open Math,2017,15(1):1267-1276.
[12]WANG Y N,WANG G. Two S-type Z-eigenvalue inclusion sets for tensors[J]. J Inequal Appl,2017,2017(1):152.
[13]SANG C L. A new Brauer-type Z-eigenvalue inclusion set for tensors[J]. Numerical Algorithms,2018(1):1-14.
[14]ZHAO J X. A new Z-eigenvalue localization set for tensors[J]. J Inequal Appl,2017,2017(1):85.
[15]HE J,HUANG T Z. Upper bound for the largest Z-eigenvalue of positive tensors[J]. Appl Math Lett,2014,38:110-114.
[16]LI W,LIU W H,VONG S W. Some bounds for H-eigenpairs and Z-eigenpairs of a tensors[J]. J Comput Anal Appl,2018,342:37-57.
[17]ZHAO R J,ZHENG B,LING M L. On the estimates of the Z-eigenpair for an irredueible nonnegative[J]. J Math Anal Appl,2017,450(2):1157-1179.
[18]LI C Q,LI Y T. An eigenvalue localization set for tensors with applications to determine the positive(semi-)definitenss of tensors[J]. Linear Multilinear Algebra,2016,64(4):587-601.
[2]QI L Q. Eigenvalues of a real supersymmetric tensor[J]. J Symb Comput,2005,40(6):1302-1324.
[3]LIM L H. Singular values and eigenvalues of tensors:a variational approach[C]//IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing. Puerto Vallarta,Mexico:IEEE,2005:129-132.
[4]ZHANG T,GOLUB G H. Rank-one approximation to higher order tensors[J]. SIAM J Matrix Anal Appl,2001,23(2):534-550.
[5]SONG Y S,QI L Q. Spectral properties of positively homogeneous operators induced by higher order tensors[J]. SIAM J Matrix Anal Appl,2013,34(4):1581-1595.
[6]LI W,LIU D D,VONG S W. Z-eigenpair bounds for an irreducible nonnegative tensor[J]. Linear Algebra Appl,2015,483:182-199.
[7]HE J. Bounds for the largest eigenvalue of nonnegative tensors[J]. J Comput Anal Appl,2016,20(7):1290-1301.
[8]HE J,LIU Y M,KE H,et al. Bounds for the Z-spectral radius of nonnegative tensors[J]. Springer Plus,2016,5(1):1727.
[9]LIU Q L,LI Y T. Bounds for the Z-eigenpair of general nonnegative tensors[J]. Open Math,2016,14(1):181-194.
[10]WANG G,ZHOU G L,CACCETTA L. Z-eigenvalue inclusion theorems for tensors[J]. Discrete Contin Dyn Syst,2017,B22(1):187-198.
[11]ZHAO J X,SANG C L. Two new eigenvalue localization sets for tensors and theirs applications[J]. Open Math,2017,15(1):1267-1276.
[12]WANG Y N,WANG G. Two S-type Z-eigenvalue inclusion sets for tensors[J]. J Inequal Appl,2017,2017(1):152.
[13]SANG C L. A new Brauer-type Z-eigenvalue inclusion set for tensors[J]. Numerical Algorithms,2018(1):1-14.
[14]ZHAO J X. A new Z-eigenvalue localization set for tensors[J]. J Inequal Appl,2017,2017(1):85.
[15]HE J,HUANG T Z. Upper bound for the largest Z-eigenvalue of positive tensors[J]. Appl Math Lett,2014,38:110-114.
[16]LI W,LIU W H,VONG S W. Some bounds for H-eigenpairs and Z-eigenpairs of a tensors[J]. J Comput Anal Appl,2018,342:37-57.
[17]ZHAO R J,ZHENG B,LING M L. On the estimates of the Z-eigenpair for an irredueible nonnegative[J]. J Math Anal Appl,2017,450(2):1157-1179.
[18]LI C Q,LI Y T. An eigenvalue localization set for tensors with applications to determine the positive(semi-)definitenss of tensors[J]. Linear Multilinear Algebra,2016,64(4):587-601.