{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,11]],"date-time":"2026-02-11T19:58:52Z","timestamp":1770839932285,"version":"3.50.1"},"reference-count":74,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T00:00:00Z","timestamp":1570579200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T00:00:00Z","timestamp":1570579200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"Doctoral Scientific Research Foundation of Guizhou Normal University in 2017","award":["GZNUD [2017]26"],"award-info":[{"award-number":["GZNUD [2017]26"]}]},{"name":"Innovation Program of Shanghai Municipal Education Commission"},{"name":"Program for Excellent Young Talents in Yunnan University"},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11771099"],"award-info":[{"award-number":["11771099"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Key Laboratory of Contemporary Applied Mathematics","award":["KBH1411209"],"award-info":[{"award-number":["KBH1411209"]}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11601473"],"award-info":[{"award-number":["11601473"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Applied Basic Research Programs of Science and Technology Department of Yunnan Province","award":["2018FB001"],"award-info":[{"award-number":["2018FB001"]}]},{"name":"Outstanding Youth Cultivation Project for Yunnan Province","award":["2018YDJQ021"],"award-info":[{"award-number":["2018YDJQ021"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2019,12]]},"DOI":"10.1007\/s40314-019-0958-6","type":"journal-article","created":{"date-parts":[[2019,10,9]],"date-time":"2019-10-09T13:04:25Z","timestamp":1570626265000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Pseudospectra localizations for generalized tensor eigenvalues to seek more positive definite tensors"],"prefix":"10.1007","volume":"38","author":[{"given":"Chaoqian","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qilong","family":"Liu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yimin","family":"Wei","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,10,9]]},"reference":[{"issue":"5","key":"958_CR1","doi-asserted-by":"publisher","first-page":"307","DOI":"10.1109\/TASSP.1974.1162592","volume":"22","author":"N Bose","year":"1974","unstructured":"Bose N, Kamat P (1974) Algorithm for stability test of multidimensional filters. IEEE Trans Acoust Speech Signal Process 22(5):307\u2013314","journal-title":"IEEE Trans Acoust Speech Signal Process"},{"issue":"5","key":"958_CR2","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1109\/TAC.1976.1101356","volume":"21","author":"N Bose","year":"1976","unstructured":"Bose N, Modarressi A (1976) General procedure for multivariable polynomial positivity test with control applications. IEEE Trans Auto Control 21(5):696\u2013701","journal-title":"IEEE Trans Auto Control"},{"issue":"1","key":"958_CR3","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1215\/S0012-7094-47-01403-8","volume":"14","author":"A Brauer","year":"1947","unstructured":"Brauer A et al (1947) Limits for the characteristic roots of a matrix. II. Duke Math J 14(1):21\u201326","journal-title":"Duke Math J"},{"issue":"2","key":"958_CR4","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1080\/03081088208817439","volume":"11","author":"RA Brualdi","year":"1982","unstructured":"Brualdi RA (1982) Matrices eigenvalues, and directed graphs. Linear Multilinear Algebra 11(2):143\u2013165","journal-title":"Linear Multilinear Algebra"},{"key":"958_CR5","doi-asserted-by":"publisher","first-page":"168","DOI":"10.1016\/j.laa.2015.04.034","volume":"480","author":"C Bu","year":"2015","unstructured":"Bu C, Wei Y, Sun L, Zhou J (2015) Brualdi-type eigenvalue inclusion sets of tensors. Linear Algebra Appl 480:168\u2013175","journal-title":"Linear Algebra Appl"},{"key":"958_CR6","doi-asserted-by":"publisher","first-page":"234","DOI":"10.1016\/j.laa.2016.09.041","volume":"512","author":"C Bu","year":"2017","unstructured":"Bu C, Jin X, Li H, Deng C (2017) Brauer-type eigenvalue inclusion sets and the spectral radius of tensors. Linear Algebra Appl 512:234\u2013248","journal-title":"Linear Algebra Appl"},{"issue":"2","key":"958_CR7","doi-asserted-by":"publisher","first-page":"507","DOI":"10.4310\/CMS.2008.v6.n2.a12","volume":"6","author":"KC Chang","year":"2008","unstructured":"Chang KC, Pearson K, Zhang T (2008) Perron-Frobenius theorem for nonnegative tensors. Commun Math Sci 6(2):507\u2013520","journal-title":"Commun Math Sci"},{"issue":"1","key":"958_CR8","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1016\/j.jmaa.2008.09.067","volume":"350","author":"KC Chang","year":"2009","unstructured":"Chang KC, Pearson K, Zhang T (2009) On eigenvalue problems of real symmetric tensors. J Math Anal Appl 350(1):416\u2013422","journal-title":"J Math Anal Appl"},{"key":"958_CR9","doi-asserted-by":"publisher","first-page":"536","DOI":"10.1016\/j.laa.2017.07.026","volume":"533","author":"M Che","year":"2017","unstructured":"Che M, Li G, Qi L, Wei Y (2017a) Pseudo-spectra theory of tensors and tensor polynomial eigenvalue problems. Linear Algebra Appl 533:536\u2013572","journal-title":"Linear Algebra Appl"},{"key":"958_CR10","doi-asserted-by":"publisher","first-page":"547","DOI":"10.1016\/j.cam.2016.12.022","volume":"317","author":"M Che","year":"2017","unstructured":"Che M, Qi L, Wei Y (2017b) Iterative algorithms for computing us-and u-eigenpairs of complex tensors. J Comput Appl Math 317:547\u2013564","journal-title":"J Comput Appl Math"},{"issue":"4","key":"958_CR11","doi-asserted-by":"publisher","first-page":"1263","DOI":"10.3934\/jimo.2015.11.1263","volume":"11","author":"H Chen","year":"2015","unstructured":"Chen H, Qi L (2015) Positive definiteness and semi-definiteness of even order symmetric cauchy tensors. J Ind Manag Optim 11(4):1263\u20131274","journal-title":"J Ind Manag Optim"},{"issue":"3","key":"958_CR12","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1137\/110843526","volume":"6","author":"Y Chen","year":"2013","unstructured":"Chen Y, Dai Y, Han D, Sun W (2013) Positive semidefinite generalized diffusion tensor imaging via quadratic semidefinite programming. SIAM J Imaging Sci 6(3):1531\u20131552","journal-title":"SIAM J Imaging Sci"},{"key":"958_CR13","volume-title":"Markov chains: models, algorithms and applications (international series in operations research & management science)","author":"WK Ching","year":"2006","unstructured":"Ching WK, Ng MK, Ching W (2006) Markov chains: models, algorithms and applications (international series in operations research & management science). Springer, Berlin"},{"issue":"4","key":"958_CR14","doi-asserted-by":"publisher","first-page":"1582","DOI":"10.1137\/140962292","volume":"35","author":"CF Cui","year":"2014","unstructured":"Cui CF, Dai YH, Nie J (2014) All real eigenvalues of symmetric tensors. SIAM J Matrix Anal Appl 35(4):1582\u20131601","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"3","key":"958_CR15","doi-asserted-by":"publisher","first-page":"1084","DOI":"10.1137\/06066518X","volume":"30","author":"V De Silva","year":"2008","unstructured":"De Silva V, Lim LH (2008) Tensor rank and the ill-posedness of the best low-rank approximation problem. SIAM J Matrix Anal Appl 30(3):1084\u20131127","journal-title":"SIAM J Matrix Anal Appl"},{"key":"958_CR16","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/j.laa.2018.06.032","volume":"556","author":"C Deng","year":"2018","unstructured":"Deng C, Li H, Bu C (2018) Brauer-type eigenvalue inclusion sets of stochastic\/irreducible tensors and positive definiteness of tensors. Linear Algebra Appl 556:55\u201369","journal-title":"Linear Algebra Appl"},{"issue":"3","key":"958_CR17","doi-asserted-by":"publisher","first-page":"1073","DOI":"10.1137\/140975656","volume":"36","author":"W Ding","year":"2015","unstructured":"Ding W, Wei Y (2015) Generalized tensor eigenvalue problems. SIAM J Matrix Anal Appl 36(3):1073\u20131099","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"10","key":"958_CR18","doi-asserted-by":"publisher","first-page":"3264","DOI":"10.1016\/j.laa.2013.08.038","volume":"439","author":"W Ding","year":"2013","unstructured":"Ding W, Qi L, Wei Y (2013) M-tensors and nonsingular M-tensors. Linear Algebra Appl 439(10):3264\u20133278","journal-title":"Linear Algebra Appl"},{"issue":"6","key":"958_CR19","doi-asserted-by":"publisher","first-page":"989","DOI":"10.1002\/nla.2064","volume":"23","author":"W Ding","year":"2016","unstructured":"Ding W, Hou Z, Wei Y (2016) Tensor logarithmic norm and its applications. Numer Linear Algebra 23(6):989\u20131006","journal-title":"Numer Linear Algebra"},{"issue":"1","key":"958_CR20","doi-asserted-by":"publisher","first-page":"67","DOI":"10.13001\/1081-3810.1489","volume":"22","author":"S Friedland","year":"2011","unstructured":"Friedland S, Mehrmann V, Miedlar A, Nkengla M (2011) Fast low rank approximations of matrices and tensors. Electron J Linear Algebra 22(1):67","journal-title":"Electron J Linear Algebra"},{"issue":"10","key":"958_CR21","doi-asserted-by":"publisher","first-page":"1430","DOI":"10.1109\/9.720500","volume":"43","author":"M Fu","year":"1998","unstructured":"Fu M (1998) Comments on \u201ca procedure for the positive definiteness of forms of even order\u201d. IEEE Trans Auto Control 43(10):1430","journal-title":"IEEE Trans Auto Control"},{"issue":"2","key":"958_CR22","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1109\/TAC.1964.1105654","volume":"9","author":"R Gadenz","year":"1964","unstructured":"Gadenz R, Li C (1964) On positive definiteness of quartic forms of two variables. IEEE Trans Auto Control 9(2):187\u2013188","journal-title":"IEEE Trans Auto Control"},{"key":"958_CR23","first-page":"749","volume":"6","author":"SA Gershgorin","year":"1931","unstructured":"Gershgorin SA (1931) Uber die abgrenzung der eigenwerte einer matrix. Izv Akad Nauk SSSR Ser Mat 6:749\u2013754","journal-title":"Izv Akad Nauk SSSR Ser Mat"},{"key":"958_CR24","unstructured":"Golub G, Loan CV (2013) Matrix computations (4th edn), Johns Hopkins studies in the mathematical sciences. Johns Hopkins University Press, Baltimore"},{"issue":"4","key":"958_CR25","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1109\/9.489287","volume":"41","author":"MA Hasan","year":"1996","unstructured":"Hasan MA, Hasan AA (1996) A procedure for the positive definiteness of forms of even order. IEEE Trans Auto Control 41(4):615\u2013617","journal-title":"IEEE Trans Auto Control"},{"issue":"6","key":"958_CR26","doi-asserted-by":"publisher","first-page":"45","DOI":"10.1145\/2512329","volume":"60","author":"CJ Hillar","year":"2013","unstructured":"Hillar CJ, Lim LH (2013) Most tensor problems are np-hard. J ACM 60(6):45","journal-title":"J ACM"},{"issue":"4","key":"958_CR27","doi-asserted-by":"publisher","first-page":"564","DOI":"10.1007\/s10878-011-9407-1","volume":"24","author":"S Hu","year":"2012","unstructured":"Hu S, Qi L (2012) Algebraic connectivity of an even uniform hypergraph. J Comb Optim 24(4):564\u2013579","journal-title":"J Comb Optim"},{"key":"958_CR28","doi-asserted-by":"publisher","first-page":"140","DOI":"10.1016\/j.dam.2013.12.024","volume":"169","author":"S Hu","year":"2014","unstructured":"Hu S, Qi L (2014) The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph. Discrete Appl Math 169:140\u2013151","journal-title":"Discrete Appl Math"},{"key":"958_CR29","doi-asserted-by":"publisher","first-page":"57","DOI":"10.3934\/ipi.2012.6.57","volume":"6","author":"S Hu","year":"2012","unstructured":"Hu S, Huang Z, Ni H, Qi L (2012) Positive definiteness of diffusion kurtosis imaging. Inverse Probl Imaging 6:57\u201375","journal-title":"Inverse Probl Imaging"},{"issue":"10","key":"958_CR30","doi-asserted-by":"publisher","first-page":"2980","DOI":"10.1016\/j.laa.2013.08.028","volume":"439","author":"S Hu","year":"2013","unstructured":"Hu S, Qi L, Shao JY (2013) Cored hypergraphs, power hypergraphs and their Laplacian h-eigenvalues. Linear Algebra Its Appl 439(10):2980\u20132998","journal-title":"Linear Algebra Its Appl"},{"issue":"1","key":"958_CR31","doi-asserted-by":"publisher","first-page":"012304","DOI":"10.1103\/PhysRevA.93.012304","volume":"93","author":"S Hu","year":"2016","unstructured":"Hu S, Qi L, Zhang G (2016) Computing the geometric measure of entanglement of multipartite pure states by means of non-negative tensors. Phys Rev A 93(1):012304","journal-title":"Phys Rev A"},{"issue":"1","key":"958_CR32","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/s40305-016-0135-1","volume":"5","author":"B Hua","year":"2017","unstructured":"Hua B, Ni GY, Zhang MS (2017) Computing geometric measure of entanglement for symmetric pure states via the Jacobian sdp relaxation technique. J Oper Res Soc China 5(1):111\u2013121","journal-title":"J Oper Res Soc China"},{"key":"958_CR33","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.laa.2015.02.034","volume":"476","author":"MR Kannan","year":"2015","unstructured":"Kannan MR, Shaked-Monderer N, Berman A (2015) Some properties of strong h-tensors and general h-tensors. Linear Algebra Appl 476:42\u201355","journal-title":"Linear Algebra Appl"},{"issue":"3","key":"958_CR34","doi-asserted-by":"publisher","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda TG, Bader BW (2009) Tensor decompositions and applications. SIAM Rev 51(3):455\u2013500","journal-title":"SIAM Rev"},{"issue":"4","key":"958_CR35","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1137\/100801482","volume":"32","author":"TG Kolda","year":"2011","unstructured":"Kolda TG, Mayo JR (2011) Shifted power method for computing tensor eigenpairs. SIAM J Matrix Anal Appl 32(4):1095\u20131124","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"4","key":"958_CR36","doi-asserted-by":"publisher","first-page":"1563","DOI":"10.1137\/140951758","volume":"35","author":"TG Kolda","year":"2014","unstructured":"Kolda TG, Mayo JR (2014) An adaptive shifted power method for computing generalized tensor eigenpairs. SIAM J Matrix Anal Appl 35(4):1563\u20131581","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"11\u201312","key":"958_CR37","doi-asserted-by":"publisher","first-page":"883","DOI":"10.1002\/nla.671","volume":"16","author":"V Kosti\u0107","year":"2009","unstructured":"Kosti\u0107 V, Cvetkovi\u0107 L, Varga RS (2009) Ger\u0161gorin-type localizations of generalized eigenvalues. Numer Linear Algebra 16(11\u201312):883\u2013898","journal-title":"Numer Linear Algebra"},{"issue":"2","key":"958_CR38","doi-asserted-by":"publisher","first-page":"356","DOI":"10.1002\/nla.2028","volume":"23","author":"V Kosti\u0107","year":"2016","unstructured":"Kosti\u0107 V, Cvetkovi\u0107 L, Cvetkovi\u0107 DL (2016) Pseudospectra localizations and their applications. Numer Linear Algebra 23(2):356\u2013372","journal-title":"Numer Linear Algebra"},{"issue":"3","key":"958_CR39","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1109\/TAC.1965.1098177","volume":"10","author":"W Ku","year":"1965","unstructured":"Ku W (1965) Explicit criterion for the positive definiteness of a general quartic form. IEEE Trans Auto Control 10(3):372\u2013373","journal-title":"IEEE Trans Auto Control"},{"key":"958_CR40","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1016\/j.laa.2014.10.027","volume":"466","author":"C Li","year":"2015","unstructured":"Li C, Li Y (2015) Double b-tensors and quasi-double B-tensors. Linear Algebra Appl 466:343\u2013356","journal-title":"Linear Algebra Appl"},{"issue":"4","key":"958_CR41","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1080\/03081087.2015.1049582","volume":"64","author":"C Li","year":"2016","unstructured":"Li C, Li Y (2016) An eigenvalue localization set for tensors with applications to determine the positive (semi-) definiteness of tensors. Linear Multilinear A 64(4):587\u2013601","journal-title":"Linear Multilinear A"},{"issue":"1","key":"958_CR42","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1002\/nla.1858","volume":"21","author":"C Li","year":"2014","unstructured":"Li C, Li Y, Kong X (2014a) New eigenvalue inclusion sets for tensors. Numer Linear Algebra 21(1):39\u201350","journal-title":"Numer Linear Algebra"},{"key":"958_CR43","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.cam.2013.04.022","volume":"255","author":"C Li","year":"2014","unstructured":"Li C, Wang F, Zhao J, Zhu Y, Li Y (2014b) Criterions for the positive definiteness of real supersymmetric tensors. J Comput Appl Math 255:1\u201314","journal-title":"J Comput Appl Math"},{"key":"958_CR44","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1016\/j.laa.2015.06.030","volume":"484","author":"C Li","year":"2015","unstructured":"Li C, Qi L, Li Y (2015) MB-tensors and MB$$_0$$-tensors. Linear Algebra Appl 484:141\u2013153","journal-title":"Linear Algebra Appl"},{"key":"958_CR45","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1016\/j.laa.2015.12.018","volume":"493","author":"C Li","year":"2016","unstructured":"Li C, Jiao A, Li Y (2016) An S-type eigenvalue localization set for tensors. Linear Algebra Appl 493:469\u2013483","journal-title":"Linear Algebra Appl"},{"issue":"3","key":"958_CR46","doi-asserted-by":"publisher","first-page":"362","DOI":"10.1080\/03081087.2013.777436","volume":"62","author":"W Li","year":"2014","unstructured":"Li W, Ng MK (2014) On the limiting probability distribution of a transition probability tensor. Linear Multilinear A 62(3):362\u2013385","journal-title":"Linear Multilinear A"},{"key":"958_CR47","unstructured":"Lim LH (2005) Singular values and eigenvalues of tensors: a variational approach. In: 1st IEEE international workshop on computational advances in multi-sensor adaptive processing, 2005. IEEE, pp 129\u2013132"},{"key":"958_CR48","volume-title":"Spectrum and pseudospectrum of a tensor","author":"LH Lim","year":"2008","unstructured":"Lim LH (2008) Spectrum and pseudospectrum of a tensor. University of California, Berkeley"},{"key":"958_CR49","doi-asserted-by":"crossref","unstructured":"Liu L, Wu W (2006) Dynamical system for computing largest generalized eigenvalue. In: International symposium on neural networks. Springer, pp 399\u2013404","DOI":"10.1007\/11759966_60"},{"issue":"1","key":"958_CR50","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1016\/j.cam.2010.06.002","volume":"235","author":"Y Liu","year":"2010","unstructured":"Liu Y, Zhou G, Ibrahim NF (2010) An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor. J Comput Appl Math 235(1):286\u2013292","journal-title":"J Comput Appl Math"},{"issue":"3","key":"958_CR51","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1007\/s10589-016-9848-7","volume":"65","author":"G Ni","year":"2016","unstructured":"Ni G, Bai M (2016) Spherical optimization with complex variablesfor computing us-eigenpairs. Comput Optim Appl 65(3):799\u2013820","journal-title":"Comput Optim Appl"},{"issue":"1","key":"958_CR52","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1137\/120892891","volume":"35","author":"G Ni","year":"2014","unstructured":"Ni G, Qi L, Bai M (2014) Geometric measure of entanglement and u-eigenvalues of tensors. SIAM J Matrix Anal Appl 35(1):73\u201387","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"5","key":"958_CR53","doi-asserted-by":"publisher","first-page":"1096","DOI":"10.1109\/TAC.2008.923679","volume":"53","author":"Q Ni","year":"2008","unstructured":"Ni Q, Lq Qi, Wang F (2008) An eigenvalue method for the positive definiteness identification problem. IEEE Trans Autom Control 53(5):1096\u20131107","journal-title":"IEEE Trans Autom Control"},{"issue":"3","key":"958_CR54","doi-asserted-by":"publisher","first-page":"1155","DOI":"10.1137\/130935112","volume":"35","author":"J Nie","year":"2014","unstructured":"Nie J, Wang L (2014) Semidefinite relaxations for best rank-1 tensor approximations. SIAM J Matrix Anal Appl 35(3):1155\u20131179","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"6","key":"958_CR55","doi-asserted-by":"publisher","first-page":"1302","DOI":"10.1016\/j.jsc.2005.05.007","volume":"40","author":"L Qi","year":"2005","unstructured":"Qi L (2005) Eigenvalues of a real supersymmetric tensor. J Symb Comput 40(6):1302\u20131324","journal-title":"J Symb Comput"},{"issue":"2","key":"958_CR56","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1137\/100795802","volume":"32","author":"L Qi","year":"2011","unstructured":"Qi L (2011) The best rank-one approximation ratio of a tensor space. SIAM J Matrix Anal Appl 32(2):430\u2013442","journal-title":"SIAM J Matrix Anal Appl"},{"key":"958_CR57","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611974751","volume-title":"Tensor analysis: spectral theory and special tensors","author":"L Qi","year":"2017","unstructured":"Qi L, Luo Z (2017) Tensor analysis: spectral theory and special tensors, vol 151. SIAM, Philadelphia"},{"key":"958_CR58","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1016\/j.laa.2014.05.026","volume":"457","author":"L Qi","year":"2014","unstructured":"Qi L, Song Y (2014) An even order symmetric b tensor is positive definite. Linear Algebra Appl 457:303\u2013312","journal-title":"Linear Algebra Appl"},{"issue":"1","key":"958_CR59","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.cam.2007.10.012","volume":"221","author":"L Qi","year":"2008","unstructured":"Qi L, Wang Y, Wu EX (2008) D-eigenvalues of diffusion kurtosis tensors. J Comput Appl Math 221(1):150\u2013157","journal-title":"J Comput Appl Math"},{"issue":"3","key":"958_CR60","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1137\/090755138","volume":"3","author":"L Qi","year":"2010","unstructured":"Qi L, Yu G, Wu EX (2010a) Higher order positive semidefinite diffusion tensor imaging. SIAM J Imaging Sci 3(3):416\u2013433","journal-title":"SIAM J Imaging Sci"},{"issue":"3","key":"958_CR61","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1137\/090755138","volume":"3","author":"L Qi","year":"2010","unstructured":"Qi L, Yu G, Wu EX (2010b) Higher order positive semidefinite diffusion tensor imaging. SIAM J Imaging Sci 3(3):416\u2013433","journal-title":"SIAM J Imaging Sci"},{"issue":"3","key":"958_CR62","doi-asserted-by":"publisher","first-page":"781","DOI":"10.1007\/s11075-018-0506-2","volume":"80","author":"C Sang","year":"2019","unstructured":"Sang C (2019) A new Brauer-type Z-eigenvalue inclusion set for tensors. Numer Algorithms 80(3):781\u2013794","journal-title":"Numer Algorithms"},{"key":"958_CR63","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.laa.2014.03.023","volume":"451","author":"Y Song","year":"2014","unstructured":"Song Y, Qi L (2014) Infinite and finite dimensional Hilbert tensors. Linear Algebra Appl 451:1\u201314","journal-title":"Linear Algebra Appl"},{"issue":"3","key":"958_CR64","doi-asserted-by":"publisher","first-page":"854","DOI":"10.1007\/s10957-014-0616-5","volume":"165","author":"Y Song","year":"2015","unstructured":"Song Y, Qi L (2015) Properties of some classes of structured tensors. J Optim Theory Appl 165(3):854\u2013873","journal-title":"J Optim Theory Appl"},{"key":"958_CR65","doi-asserted-by":"crossref","unstructured":"Sun L, Ji S, Ye J (2008) Hypergraph spectral learning for multi-label classification. In: Proceedings of the 14th ACM SIGKDD international conference on knowledge discovery and data mining, ACM, pp 668\u2013676","DOI":"10.1145\/1401890.1401971"},{"key":"958_CR66","volume-title":"Ger\u0161gorin and his circles","author":"RS Varga","year":"2010","unstructured":"Varga RS (2010) Ger\u0161gorin and his circles, vol 36. Springer Science & Business Media, Berlin"},{"issue":"3","key":"958_CR67","doi-asserted-by":"publisher","first-page":"416","DOI":"10.1109\/TAC.2005.843851","volume":"50","author":"F Wang","year":"2005","unstructured":"Wang F, Qi L (2005) Comments on \u201cexplicit criterion for the positive definiteness of a general quartic form\u201d. IEEE Trans Autom Control 50(3):416\u2013418","journal-title":"IEEE Trans Autom Control"},{"key":"958_CR68","first-page":"187","volume":"22","author":"G Wang","year":"2017","unstructured":"Wang G, Zhou G, Caccetta L (2017) Z-eigenvalue inclusion theorems for tensors. Discrete Cont Dyn-B 22:187\u2013198","journal-title":"Discrete Cont Dyn-B"},{"issue":"2","key":"958_CR69","doi-asserted-by":"publisher","first-page":"e2136","DOI":"10.1002\/nla.2136","volume":"25","author":"X Wang","year":"2018","unstructured":"Wang X, Navasca C (2018) Low-rank approximation of tensors via sparse optimization. Numer Linear Algebra 25(2):e2136","journal-title":"Numer Linear Algebra"},{"issue":"1","key":"958_CR70","doi-asserted-by":"publisher","first-page":"152","DOI":"10.1186\/s13660-017-1428-6","volume":"2017","author":"Y Wang","year":"2017","unstructured":"Wang Y, Wang G (2017) Two s-type z-eigenvalue inclusion sets for tensors. J Inequal Appl 2017(1):152","journal-title":"J Inequal Appl"},{"issue":"4","key":"958_CR71","doi-asserted-by":"publisher","first-page":"042307","DOI":"10.1103\/PhysRevA.68.042307","volume":"68","author":"TC Wei","year":"2003","unstructured":"Wei TC, Goldbart PM (2003) Geometric measure of entanglement and applications to bipartite and multipartite quantum states. Phys Rev A 68(4):042307","journal-title":"Phys Rev A"},{"key":"958_CR72","volume-title":"Theory and computation of tensors: multi-dimensional arrays","author":"Y Wei","year":"2016","unstructured":"Wei Y, Ding W (2016) Theory and computation of tensors: multi-dimensional arrays. Academic Press, Cambridge"},{"issue":"1","key":"958_CR73","doi-asserted-by":"publisher","first-page":"40","DOI":"10.1109\/TPAMI.2007.250598","volume":"29","author":"S Yan","year":"2007","unstructured":"Yan S, Xu D, Zhang B, Zhang HJ, Yang Q, Lin S (2007) Graph embedding and extensions: a general framework for dimensionality reduction. IEEE Trans Pattern Anal Mach Intell 29(1):40\u201351","journal-title":"IEEE Trans Pattern Anal Mach Intell"},{"issue":"2","key":"958_CR74","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1137\/130915339","volume":"35","author":"L Zhang","year":"2014","unstructured":"Zhang L, Qi L, Zhou G (2014) M-tensors and some applications. SIAM J Matrix Anal Appl 35(2):437\u2013452","journal-title":"SIAM J Matrix Anal Appl"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-0958-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-019-0958-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-019-0958-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,7]],"date-time":"2020-10-07T23:37:41Z","timestamp":1602113861000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-019-0958-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,9]]},"references-count":74,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["958"],"URL":"https:\/\/doi.org\/10.1007\/s40314-019-0958-6","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,10,9]]},"assertion":[{"value":"31 May 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 July 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 September 2019","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"9 October 2019","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"183"}}