New criteria for H-tensors and an application
Feng Wang ; Deshu Sun
Open Mathematics, Tome 13 (2015), / Harvested from The Polish Digital Mathematics Library
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Some new criteria for identifying H-tensors are obtained. As an application, some sufficient conditions of the positive definiteness for an even-order real symmetric tensor are given. Advantages of results obtained are illustrated by numerical examples.

Publié le : 2015-01-01
EUDML-ID : urn:eudml:doc:275959 
@article{bwmeta1.element.doi-10_1515_math-2015-0058,
     author = {Feng Wang and Deshu Sun},
     title = {New criteria for H-tensors and an application},
     journal = {Open Mathematics},
     volume = {13},
     year = {2015},
     zbl = {06613691},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2015-0058}
}

Feng Wang; Deshu Sun. New criteria for H-tensors and an application. Open Mathematics, Tome 13 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2015-0058/

[1] Qi, L.: Eigenvalues of a real supersymetric tensor. J. Symbolic Comput. 40 (2005), 1302-1324. | Zbl 1125.15014

[2] Kannana, M.R., Mondererb, N.S., Bermana, A.: Some properties of strong H-tensors and general H-tensors. Linear Algebra Appl. 476 (2015), 42-55. [WoS]

[3] Li, C. Q., Qi, L., Li, Y.T.:MB-tensors andMB0-tensors. Linear Algebra Appl. 484(2015), 141-153. | Zbl 1325.15022

[4] Yang, Y., Yang, Q.:Fruther results for Perron-Frobenius theorem for nonnegative tensors. SIAM. J. Mayrix Anal. Appl. 31 (2010), 2517-2530. | Zbl 1227.15014

[5] Kolda, T.G., Mayo, J.R.:Shifted power method for computing tensor eigenpairs. SIAM J. Matrix Anal. Appl. 32 (4) (2011), 1095- 1124. [Crossref][WoS] | Zbl 1247.65048

[6] Lim, L.H.: Singular values and eigenvalues of tensors: a variational approach, in: CAMSAP’05: Proceeding of the IEEE International Workshop on Computational Advances in MultiSensor Adaptive Processing, 2005, pp. 129-132.

[7] Qi, L.:Eigenvalues and invariants of tensors. J. Math. Anal. Appl. 325 (2007), 1363-1377. | Zbl 1113.15020

[8] Ni, Q., Qi, L., Wang, F.:An eigenvalue method for the positive definiteness identification problem. IEEE Trans. Automat. Control. 53 (2008), 1096-1107.

[9] Ni, G., Qi, L., Wang, F., Wang, Y.:The degree of the E-characteristic polynomial of an even order tensor. J. Math. Anal. Appl. 329(2007), 1218-1229. | Zbl 1154.15304

[10] Zhang, L., Qi, L., Zhou, G.:M-tensors and some applications. SIAM J. Matrix Anal. Appl. 32(2014), 437-452. | Zbl 1307.15034

[11] Ding, W., Qi, L., Wei, Y.:M-tensors and nonsingular M-tensors. Linear Algebra Appl. 439 (2013), 3264-3278. | Zbl 1283.15074

[12] Li, C. Q., Wang, F., Zhao, J.X., Zhu, Y., Li, Y.T.: Criterions for the positive definiteness of real supersymmetric tensors. J. Comput. Appl. Math. 255(2014), 1-14. [WoS] | Zbl 1291.15065