{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:54:48Z","timestamp":1740142488215,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T00:00:00Z","timestamp":1614556800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T00:00:00Z","timestamp":1614556800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The improvements of Ky Fan theorem are given for tensors. First, based on Brauer-type eigenvalue inclusion sets, we obtain some new Ky Fan-type theorems for tensors. Second, by characterizing the ratio of the smallest and largest values of a Perron vector, we improve the existing results. Third, some new eigenvalue localization sets for tensors are given and proved to be tighter than those presented by Li and Ng (Numer Math 130(2):315\u2013335, 2015) and Wang et al. (Linear Multilinear Algebra 68(9):1817\u20131834, 2020). Finally, numerical examples are given to validate the efficiency of our new bounds.<\/jats:p>","DOI":"10.1007\/s40314-020-01396-0","type":"journal-article","created":{"date-parts":[[2021,3,1]],"date-time":"2021-03-01T09:03:11Z","timestamp":1614589391000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some improvements on the Ky Fan theorem for tensors"],"prefix":"10.1007","volume":"40","author":[{"given":"Mohsen","family":"Tourang","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4472-3609","authenticated-orcid":false,"given":"Mostafa","family":"Zangiabadi","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,3,1]]},"reference":[{"issue":"1","key":"1396_CR1","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 (1947) Limits for the characteristic roots of a matrix II. Duke Math J 14(1):21\u201326","journal-title":"Duke Math J"},{"key":"1396_CR2","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":"1396_CR3","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\u2013Frobenius theorem for nonnegative tensors. Commun Math Sci 6(2):507\u2013520","journal-title":"Commun Math Sci"},{"issue":"3","key":"1396_CR4","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1215\/S0012-7094-58-02538-9","volume":"25","author":"K Fan","year":"1958","unstructured":"Fan K (1958) Note on circular disks containing the eigenvalues of a matrix. Duke Math J 25(3):441\u2013445","journal-title":"Duke Math J"},{"key":"1396_CR5","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139020411","volume-title":"Matrix analysis","author":"RA Horn","year":"2012","unstructured":"Horn RA, Johnson CR (2012) Matrix analysis. Cambridge University Press, Cambridge"},{"issue":"5\u20136","key":"1396_CR6","doi-asserted-by":"publisher","first-page":"789","DOI":"10.1016\/j.camwa.2004.07.019","volume":"49","author":"HB Li","year":"2005","unstructured":"Li HB, Huang TZ (2005) An improvement of Ky Fan theorem for matrix eigenvalues. Comput Math Appl 49(5\u20136):789\u2013803","journal-title":"Comput Math Appl"},{"issue":"4","key":"1396_CR7","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 Algebra 64(4):587\u2013601","journal-title":"Linear Multilinear Algebra"},{"key":"1396_CR8","doi-asserted-by":"publisher","first-page":"71","DOI":"10.1016\/j.laa.2016.02.002","volume":"496","author":"C Li","year":"2016","unstructured":"Li C, Li Y (2016) Relationships between Brauer-type eigenvalue inclusion sets and a Brualdi-type eigenvalue inclusion set for tensors. Linear Algebra Appl 496:71\u201380","journal-title":"Linear Algebra Appl"},{"issue":"2","key":"1396_CR9","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/s00211-014-0666-5","volume":"130","author":"W Li","year":"2015","unstructured":"Li W, Ng MK (2015) Some bounds for the spectral radius of nonnegative tensors. Numer Math 130(2):315\u2013335","journal-title":"Numer Math"},{"issue":"1","key":"1396_CR10","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 (2014) New eigenvalue inclusion sets for tensors. Numer Linear Algebra Appl 21(1):39\u201350","journal-title":"Numer Linear Algebra Appl"},{"key":"1396_CR11","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/s40314-020-01245-0","volume":"39","author":"S Li","year":"2020","unstructured":"Li S, Chen Z, Li C, Zhao J (2020) Eigenvalue bounds of third-order tensors via the minimax eigenvalue of symmetric matrices. Comput Appl Math 39:217","journal-title":"Comput Appl Math"},{"issue":"2","key":"1396_CR12","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1007\/s40314-019-0853-1","volume":"38","author":"Q Liu","year":"2019","unstructured":"Liu Q, Chen Z (2019) An algorithm for computing the spectral radius of nonnegative tensors. Comput Appl Math 38(2):90","journal-title":"Comput Appl Math"},{"issue":"6","key":"1396_CR13","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"},{"key":"1396_CR14","doi-asserted-by":"crossref","unstructured":"Qi L, Luo Z (2017) Tensor analysis: spectral theory and special tensors. SIAM, Philadelphia","DOI":"10.1137\/1.9781611974751"},{"key":"1396_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-17798-9","volume-title":"Gershgorin and his circles","author":"RS Varga","year":"2004","unstructured":"Varga RS (2004) Gershgorin and his circles. Springer Series in Computational Mathematics, New York"},{"key":"1396_CR16","doi-asserted-by":"crossref","unstructured":"Wang G, Wang Y, Wang Y (2020) Some Ostrowski-type bound estimations of spectral radius for weakly irreducible nonnegative tensors. Linear Multilinear Algebra 68(9):1817\u20131834","DOI":"10.1080\/03081087.2018.1561823"},{"key":"1396_CR17","volume-title":"Theory and computation of tensors: multi-dimensional arrays","author":"Y Wei","year":"2017","unstructured":"Wei Y, Ding W (2017) Theory and computation of tensors: multi-dimensional arrays. Academic Press, London"},{"key":"1396_CR18","doi-asserted-by":"publisher","first-page":"74","DOI":"10.1007\/s40314-019-0831-7","volume":"38","author":"Y Xu","year":"2019","unstructured":"Xu Y, Zheng B, Zhao R (2019) Some results on Brauer-type and Brualdi-type eigenvalue inclusion sets for tensors. Comput Appl Math 38:74","journal-title":"Comput Appl Math"},{"issue":"5","key":"1396_CR19","doi-asserted-by":"publisher","first-page":"2517","DOI":"10.1137\/090778766","volume":"31","author":"Y Yang","year":"2010","unstructured":"Yang Y, Yang Q (2010) Further results for Perron\u2013Frobenius theorem for nonnegative tensors. SIAM J Matrix Anal Appl 31(5):2517\u20132530","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\/s40314-020-01396-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s40314-020-01396-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01396-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,13]],"date-time":"2021-03-13T21:13:13Z","timestamp":1615669993000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s40314-020-01396-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,3]]}},"alternative-id":["1396"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01396-0","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2021,3]]},"assertion":[{"value":"3 August 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 November 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 December 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"1 March 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"65"}}