{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,12]],"date-time":"2025-07-12T01:13:26Z","timestamp":1752282806389,"version":"3.37.3"},"reference-count":37,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,4,6]],"date-time":"2018-04-06T00:00:00Z","timestamp":1522972800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"The Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11571004"],"award-info":[{"award-number":["11571004"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Fundamental Research Funds for the Central Universities, China","award":["lzujbky-2017-it54"],"award-info":[{"award-number":["lzujbky-2017-it54"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2019,4]]},"DOI":"10.1007\/s11075-018-0519-x","type":"journal-article","created":{"date-parts":[[2018,4,19]],"date-time":"2018-04-19T15:12:10Z","timestamp":1524150730000},"page":"1121-1141","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Some criteria for identifying strong \u210b $\\mathcal {H}$ -tensors"],"prefix":"10.1007","volume":"80","author":[{"given":"Yangyang","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruijuan","family":"Zhao","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bing","family":"Zheng","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,4,6]]},"reference":[{"key":"519_CR1","doi-asserted-by":"publisher","first-page":"507","DOI":"10.4310\/CMS.2008.v6.n2.a12","volume":"6","author":"KC Chang","year":"2008","unstructured":"Chang, K.C., Pearson, K., Zhang, T.: Perron-Frobenius theorem for nonnegative tensors. Commun. Math. Sci. 6, 507\u2013520 (2008)","journal-title":"Commun. Math. Sci."},{"key":"519_CR2","doi-asserted-by":"publisher","first-page":"1302","DOI":"10.1016\/j.jsc.2005.05.007","volume":"40","author":"LQ Qi","year":"2005","unstructured":"Qi, L.Q.: Eigenvalues of a real supersymmetric tensor. J. Symb. Comput. 40, 1302\u20131324 (2005)","journal-title":"J. Symb. Comput."},{"key":"519_CR3","doi-asserted-by":"publisher","first-page":"1324","DOI":"10.1137\/S0895479898346995","volume":"21","author":"LD Lathauwer","year":"2000","unstructured":"Lathauwer, L.D., Moor, B.D., Vandewalle, J.: On the best rank-1 and rank-(r 1, r 2,\u22c5\u22c5\u22c5, r n) approximation of higher-order tensors. SIAM J. Matrix Anal. Appl. 21, 1324\u20131342 (2000)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"519_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2512329","volume":"60","author":"CJ Hillar","year":"2013","unstructured":"Hillar, C.J., Lim, L.H.: Most tensor problems are NP-hard. J. ACM 60, 1\u201339 (2013)","journal-title":"J. ACM"},{"key":"519_CR5","doi-asserted-by":"publisher","first-page":"3264","DOI":"10.1016\/j.laa.2013.08.038","volume":"439","author":"WY Ding","year":"2013","unstructured":"Ding, W.Y., Qi, L.Q., Wei, Y.M.: \u2133 $\\mathcal {M}$ -tensors and nonsingular \u2133 $\\mathcal {M}$ -tensors. Linear Algebra Appl. 439, 3264\u20133278 (2013)","journal-title":"Linear Algebra Appl."},{"key":"519_CR6","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.3934\/jimo.2015.11.1263","volume":"11","author":"HB Chen","year":"2015","unstructured":"Chen, H.B., Qi, L.Q.: Positive definiteness and semi-definiteness of even order symmetric Cauchy tensors. J. Ind. Manag. Optim. 11, 1263\u20131274 (2015)","journal-title":"J. Ind. Manag. Optim."},{"key":"519_CR7","first-page":"1","volume":"114","author":"J He","year":"2014","unstructured":"He, J., Huang, T.Z.: Inequalities for \u2133 $\\mathcal {M}$ -tensors. J. Inequal. Appl. 114, 1\u20139 (2014)","journal-title":"J. Inequal. Appl."},{"key":"519_CR8","doi-asserted-by":"publisher","first-page":"113","DOI":"10.4310\/CMS.2015.v13.n1.a6","volume":"13","author":"LQ Qi","year":"2015","unstructured":"Qi, L.Q.: Hankel tensors: associated Hankel matrices and Vandermonde decomposition. Commun. Math. Sci. 13, 113\u2013125 (2015)","journal-title":"Commun. Math. Sci."},{"key":"519_CR9","doi-asserted-by":"publisher","first-page":"854","DOI":"10.1007\/s10957-014-0616-5","volume":"165","author":"YS Song","year":"2015","unstructured":"Song, Y.S., Qi, L.Q.: Properties of some classes of structured tensors. J. Optim. Theory Appl. 165, 854\u2013873 (2015)","journal-title":"J. Optim. Theory Appl."},{"key":"519_CR10","doi-asserted-by":"publisher","first-page":"511","DOI":"10.1016\/j.laa.2014.07.043","volume":"459","author":"PZ Yuan","year":"2014","unstructured":"Yuan, P.Z., You, L.H.: Some remarks on P $\\mathcal {P}$ , P 0 $\\mathcal {P}_0$ , \u212c $\\mathcal {B}$ and \u212c 0 $\\mathcal {B}_0$ tensors. Linear Algebra Appl. 459, 511\u2013521 (2014)","journal-title":"Linear Algebra Appl."},{"key":"519_CR11","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1137\/130915339","volume":"35","author":"LP Zhang","year":"2014","unstructured":"Zhang, L.P., Qi, L.Q., Zhou, G.L.: \u2133 $\\mathcal {M}$ -tensors and some applications. SIAM J. Matrix Anal. Appl. 35, 437\u2013452 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"519_CR12","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.laa.2014.05.026","volume":"457","author":"LQ Qi","year":"2014","unstructured":"Qi, L.Q., Song, Y.S.: An even order symmetric \u212c $\\mathcal {B}$ -tensor is positive definite. Linear Algebra Appl. 457, 303\u2013312 (2014)","journal-title":"Linear Algebra Appl."},{"key":"519_CR13","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.amc.2015.11.051","volume":"275","author":"HB Chen","year":"2016","unstructured":"Chen, H.B., Li, G.Y., Qi, L.Q.: Further results on Cauchy tensors and Hankel tensors. Appl. Math. Comput. 275, 50\u201362 (2016)","journal-title":"Appl. Math. Comput."},{"key":"519_CR14","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/S0024-3795(03)00646-3","volume":"374","author":"TB Gan","year":"2003","unstructured":"Gan, T.B., Huang, T.Z.: Simple criteria for nonsingular H-matrices. Linear Algebra Appl. 374, 317\u2013326 (2003)","journal-title":"Linear Algebra Appl."},{"key":"519_CR15","doi-asserted-by":"publisher","first-page":"1065","DOI":"10.1080\/00207160701472469","volume":"85","author":"JZ Liu","year":"2008","unstructured":"Liu, J.Z., He, A.Q.: Simple criteria for generalized diagonally dominant matrices. Int. J. Comput. Math. 85, 1065\u20131072 (2008)","journal-title":"Int. J. Comput. Math."},{"key":"519_CR16","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1016\/j.cam.2004.10.017","volume":"180","author":"L Cvetkovi\u0107","year":"2005","unstructured":"Cvetkovi\u0107, L., Kosti\u0107, V.: New criteria for identifying H-matrices. J. Comput. Appl. Math. 180, 265\u2013278 (2005)","journal-title":"J. Comput. Appl. Math."},{"key":"519_CR17","doi-asserted-by":"publisher","first-page":"863","DOI":"10.1080\/00207160410001712251","volume":"81","author":"TZ Huang","year":"2004","unstructured":"Huang, T.Z., Evans, D.J.: Generalized doubly diagonally dominant matrices. Int. J. Comput. Math. 81, 863\u2013870 (2004)","journal-title":"Int. J. Comput. Math."},{"key":"519_CR18","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/0024-3795(92)90182-A","volume":"169","author":"YM Gao","year":"1992","unstructured":"Gao, Y.M., Wang, X.H.: Criteria for generalized diagonally dominant matrices and M-matrices. Linear Algebra Appl. 169, 257\u2013268 (1992)","journal-title":"Linear Algebra Appl."},{"key":"519_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cam.2013.04.022","volume":"255","author":"CQ Li","year":"2014","unstructured":"Li, C.Q., Wang, F., Zhao, J.X., Li, Y.T.: Criterions for the positive definiteness of real supersymmetric tensors. J. Comput. Appl. Math. 255, 1\u201314 (2014)","journal-title":"J. Comput. Appl. Math."},{"key":"519_CR20","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1080\/03081087.2016.1183558","volume":"65","author":"F Wang","year":"2017","unstructured":"Wang, F., Sun, D.S., Zhao, J.X., Li, C.Q.: New practical criteria for \u210b $\\mathcal {H}$ -tensors and its application. Linear Multilinear Algebra 65, 269\u2013283 (2017)","journal-title":"Linear Multilinear Algebra"},{"key":"519_CR21","doi-asserted-by":"publisher","first-page":"661","DOI":"10.1007\/s11464-016-0519-x","volume":"11","author":"RJ Zhao","year":"2016","unstructured":"Zhao, R.J., Gao, L., Liu, Q.L., Li, Y.T.: Criterions for identifying \u210b $\\mathcal {H}$ -tensors. Front. Math. China 11, 661\u2013678 (2016)","journal-title":"Front. Math. China"},{"key":"519_CR22","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1007\/s11075-016-0145-4","volume":"74","author":"YT Li","year":"2017","unstructured":"Li, Y.T., Liu, Q.L., Qi, L.Q.: Programmable criteria for strong \u210b $\\mathcal {H}$ -tensors. Numer. Algorithm 74, 199\u2013221 (2017)","journal-title":"Numer. Algorithm"},{"key":"519_CR23","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.laa.2015.02.034","volume":"476","author":"MR Kannan","year":"2015","unstructured":"Kannan, M.R., Shaked-Monderer, N., Berman, A.: Some properties of strong \u210b $\\mathcal {H}$ -tensors and general \u210b $\\mathcal {H}$ -tensors. Linear Algebra Appl. 476, 42\u201355 (2015)","journal-title":"Linear Algebra Appl."},{"key":"519_CR24","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1007\/s11464-015-0495-6","volume":"11","author":"XZ Wang","year":"2016","unstructured":"Wang, X.Z., Wei, Y.M.: \u210b $\\mathcal {H}$ -tensors and nonsingular \u210b $\\mathcal {H}$ -tensors. Front. Math. China 11, 557\u2013575 (2016)","journal-title":"Front. Math. China"},{"key":"519_CR25","unstructured":"Lim, L.H.: Singular values and eigenvalues of tensors: a variational approach. In: CAMSAP\u201905: Proceedings of the IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, vol. 1, pp. 129\u2013132 (2005)"},{"key":"519_CR26","doi-asserted-by":"publisher","first-page":"1096","DOI":"10.1109\/TAC.2008.923679","volume":"53","author":"Q Ni","year":"2008","unstructured":"Ni, Q., Qi, L.Q., Wang, F.: An eigenvalue method for testing positive definiteness of a multivariate form. IEEE Trans. Automat. Control 53, 1096\u20131107 (2008)","journal-title":"IEEE Trans. Automat. Control"},{"key":"519_CR27","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1109\/TAC.1976.1101356","volume":"21","author":"NK Bose","year":"1976","unstructured":"Bose, N.K., Modarressi, A.R.: General procedure for multivariable polynomial positivity with control applications. IEEE Trans. Automat. Control 21, 696\u2013701 (1976)","journal-title":"IEEE Trans. Automat. Control"},{"key":"519_CR28","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1109\/TASSP.1974.1162592","volume":"22","author":"NK Bose","year":"1974","unstructured":"Bose, N.K., Kamat, P.S.: Algorithm for stability test of multidimensional filters. IEEE Trans. Acoust. Speech Signal Process. 22, 307\u2013314 (1974)","journal-title":"IEEE Trans. Acoust. Speech Signal Process."},{"key":"519_CR29","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1137\/110843526","volume":"6","author":"YN Chen","year":"2013","unstructured":"Chen, Y.N., Dai, Y.H., Han, D., Sun, W.Y.: Positive semidefinite generalized diffusion tensor imaging via quadratic semidefinite programming. SIAM J. Imaging Sci. 6, 1531\u20131552 (2013)","journal-title":"SIAM J. Imaging Sci."},{"key":"519_CR30","doi-asserted-by":"publisher","first-page":"57","DOI":"10.3934\/ipi.2012.6.57","volume":"6","author":"SL Hu","year":"2012","unstructured":"Hu, S.L., Huang, Z.H., Ni, H.Y., Qi, L.Q.: Positive definiteness of diffusion kurtosis imaging. Inverse Probl. Imag. 6, 57\u201375 (2012)","journal-title":"Inverse Probl. Imag."},{"key":"519_CR31","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6015-6","volume-title":"Nondifferentiable Optimization and Polynomial Problems","author":"NZ Shor","year":"1998","unstructured":"Shor, N.Z.: Nondifferentiable Optimization and Polynomial Problems. Kluwer Academic Publishers, Boston (1998)"},{"key":"519_CR32","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1007\/s10878-011-9407-1","volume":"24","author":"SL Hu","year":"2012","unstructured":"Hu, S.L., Qi, L.Q.: Algebraic connectivity of an even uniform hypergraph. J. Comb. Optim. 24, 564\u2013579 (2012)","journal-title":"J. Comb. Optim."},{"key":"519_CR33","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.dam.2013.12.024","volume":"169","author":"SL Hu","year":"2014","unstructured":"Hu, S.L., Qi, L.Q.: The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph. Discrete Appl. Math. 169, 140\u2013151 (2014)","journal-title":"Discrete Appl. Math."},{"key":"519_CR34","doi-asserted-by":"publisher","first-page":"1001","DOI":"10.1002\/nla.1877","volume":"20","author":"GY Li","year":"2013","unstructured":"Li, G.Y., Qi, L.Q., Yu, G.H.: The Z-eigenvalues of a symmetric tensor and its application to spectral hypergraph theory. Numer. Linear Algebra Appl. 20, 1001\u20131029 (2013)","journal-title":"Numer. Linear Algebra Appl."},{"key":"519_CR35","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1002\/nla.1858","volume":"21","author":"CQ Li","year":"2014","unstructured":"Li, C.Q., Li, Y.T., Kong, X.: New eigenvalue inclusion sets for tensors. Numer. Linear Algebra Appl. 21, 39\u201350 (2014)","journal-title":"Numer. Linear Algebra Appl."},{"key":"519_CR36","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1080\/03081087.2015.1049582","volume":"64","author":"CQ Li","year":"2016","unstructured":"Li, C.Q., Li, Y.T.: An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors. Linar Multilinear Algebra 64, 587\u2013601 (2016)","journal-title":"Linar Multilinear Algebra"},{"key":"519_CR37","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974751","volume-title":"Tensor Analysis: Spectral Theory and Special Tensors","author":"LQ Qi","year":"2017","unstructured":"Qi, L.Q., Luo, Z.Y.: Tensor Analysis: Spectral Theory and Special Tensors. SIAM, Philadelphia (2017)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0519-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-018-0519-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0519-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,1]],"date-time":"2020-11-01T00:40:38Z","timestamp":1604191238000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-018-0519-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4,6]]},"references-count":37,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["519"],"URL":"https:\/\/doi.org\/10.1007\/s11075-018-0519-x","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2018,4,6]]},"assertion":[{"value":"8 February 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 March 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"6 April 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}