Bounds for the M-spectral radius of a fourth-order partially symmetric tensor
Tóm tắt
M-eigenvalues of fourth-order partially symmetric tensors play an important role in many real fields such as quantum entanglement and nonlinear elastic materials analysis. In this paper, we give two bounds for the maximal absolute value of all the M-eigenvalues (called the M-spectral radius) of a fourth-order partially symmetric tensor and discuss the relation of them. A numerical example is given to explain the proposed results.
Tài liệu tham khảo
citation_journal_title=Front. Math. China; citation_title=Conditions for strong ellipticity and M-eigenvalues; citation_author=LQ Qi, HH Dai, DR Han; citation_volume=4; citation_issue=2; citation_publication_date=2009; citation_pages=349-364; citation_doi=10.1007/s11464-009-0016-6; citation_id=CR1
citation_journal_title=Int. J. Non-Linear Mech.; citation_title=Sufficient conditions for strong ellipticity for a class of anisotropic materials; citation_author=JR Walton, JP Wilber; citation_volume=38; citation_issue=4; citation_publication_date=2003; citation_pages=411-455; citation_doi=10.1016/S0020-7462(01)00066-X; citation_id=CR2
citation_journal_title=J. Elast.; citation_title=On the strong ellipticity of the anisotropic linearly elastic materials; citation_author=S Chirita, A Danescu, M Ciarletta; citation_volume=87; citation_issue=1; citation_publication_date=2007; citation_pages=1-27; citation_doi=10.1007/s10659-006-9096-7; citation_id=CR3
citation_journal_title=Linear Algebra Appl.; citation_title=A tensor product matrix approximation problem in quantum physics; citation_author=G Dahl, JM Leinaas, J Myrheim, E Ovrum; citation_volume=420; citation_issue=2–3; citation_publication_date=2007; citation_pages=711-725; citation_doi=10.1016/j.laa.2006.08.026; citation_id=CR4
citation_journal_title=Phys. Rev. Lett.; citation_title=Distinguishing separable and entangled states; citation_author=AC Doherty, PA Parillo, FM Spedalieri; citation_volume=88; citation_issue=18; citation_publication_date=2002; citation_doi=10.1103/PhysRevLett.88.187904; citation_id=CR5
citation_title=Classical deterministic complexity of Edmonds’ problem and quantum entanglement; citation_inbook_title=Proceedings of the Thirty-Fifth ACM Symposium on Theory of Computing; citation_publication_date=2003; citation_pages=10-19; citation_id=CR6; citation_author=L Gurvits; citation_publisher=ACM
citation_journal_title=J. Symb. Comput.; citation_title=Eigenvalues of a real supersymmetric tensor; citation_author=LQ Qi; citation_volume=40; citation_issue=6; citation_publication_date=2005; citation_pages=1302-1324; citation_doi=10.1016/j.jsc.2005.05.007; citation_id=CR7
citation_journal_title=J. Comput. Appl. Math.; citation_title=D-eigenvalues of diffusion kurtosis tensors; citation_author=LQ Qi, YJ Wang, EX Wu; citation_volume=221; citation_issue=1; citation_publication_date=2008; citation_pages=150-157; citation_doi=10.1016/j.cam.2007.10.012; citation_id=CR8
citation_journal_title=Numer. Linear Algebra Appl.; citation_title=A practical method for computing the largest M-eigenvalue of a fourth-order partially symmetric tensor; citation_author=YJ Wang, LQ Qi, XZ Zhang; citation_volume=16; citation_issue=7; citation_publication_date=2009; citation_pages=589-601; citation_doi=10.1002/nla.633; citation_id=CR9
Ding, WY, Liu, JJ, Qi, LQ, Yan, H: Elasticity
$\mathscr{M}$
-tensors and the strong ellipticity condition.
arXiv:1705.09911
citation_journal_title=Neural Comput.; citation_title=High-order contrasts for independent component analysis; citation_author=JF Cardoso; citation_volume=11; citation_publication_date=1999; citation_pages=157-192; citation_doi=10.1162/089976699300016863; citation_id=CR11
citation_journal_title=SIAM J. Matrix Anal. Appl.; citation_title=On the best rank-1 and rank-
approximation of higher-order tensors; citation_author=LD Lathauwer, BD Moor, J Vandewalle; citation_volume=21; citation_issue=4; citation_publication_date=2000; citation_pages=1324-1342; citation_doi=10.1137/S0895479898346995; citation_id=CR12
citation_journal_title=SIAM J. Matrix Anal. Appl.; citation_title=On the best rank-1 approximation of higher-order supersymmetric tensors; citation_author=E Kofidis, PA Regalia; citation_volume=23; citation_issue=3; citation_publication_date=2002; citation_pages=863-884; citation_doi=10.1137/S0895479801387413; citation_id=CR13
citation_journal_title=Math. Program.; citation_title=Z-eigenvalue methods for a global polynomial optimization problem; citation_author=LQ Qi, F Wang, YJ Wang; citation_volume=118; citation_publication_date=2009; citation_pages=301-316; citation_doi=10.1007/s10107-007-0193-6; citation_id=CR14