{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T08:40:45Z","timestamp":1770280845387,"version":"3.49.0"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2017,2,22]],"date-time":"2017-02-22T00:00:00Z","timestamp":1487721600000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2017,9]]},"DOI":"10.1007\/s00211-017-0869-7","type":"journal-article","created":{"date-parts":[[2017,2,22]],"date-time":"2017-02-22T16:17:16Z","timestamp":1487780236000},"page":"63-90","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":22,"title":["Newton\u2013Noda iteration for finding the Perron pair of a weakly irreducible nonnegative tensor"],"prefix":"10.1007","volume":"137","author":[{"given":"Ching-Sung","family":"Liu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chun-Hua","family":"Guo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen-Wei","family":"Lin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2017,2,22]]},"reference":[{"key":"869_CR1","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971262","volume-title":"Nonnegative Matrices in the Mathematical Sciences","author":"A Berman","year":"1994","unstructured":"Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences. SIAM, Philadelphia, PA (1994)"},{"key":"869_CR2","doi-asserted-by":"crossref","first-page":"806","DOI":"10.1137\/100807120","volume":"32","author":"K-C Chang","year":"2011","unstructured":"Chang, K.-C., Pearson, K.J., Zhang, T.: Primitivity, the convergence of the NQZ method, and the largest eigenvalue for nonnegative tensors. SIAM J. Matrix Anal. Appl. 32, 806\u2013819 (2011)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"869_CR3","doi-asserted-by":"crossref","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\u2013Frobenius theorem for nonnegative tensors. Comm. Math. Sci. 6, 507\u2013520 (2008)","journal-title":"Comm. Math. Sci."},{"key":"869_CR4","doi-asserted-by":"crossref","first-page":"3268","DOI":"10.1016\/j.laa.2011.11.018","volume":"436","author":"J Cooper","year":"2012","unstructured":"Cooper, J., Dutle, A.: Spectra of uniform hypergraphs. Linear Algebra Appl. 436, 3268\u20133292 (2012)","journal-title":"Linear Algebra Appl."},{"key":"869_CR5","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/0024-3795(76)90029-X","volume":"15","author":"L Elsner","year":"1976","unstructured":"Elsner, L.: Inverse iteration for calculating the spectral radius of a non-negative irreducible matrix. Linear Algebra Appl. 15, 235\u2013242 (1976)","journal-title":"Linear Algebra Appl."},{"key":"869_CR6","doi-asserted-by":"crossref","first-page":"738","DOI":"10.1016\/j.laa.2011.02.042","volume":"438","author":"S Friedland","year":"2013","unstructured":"Friedland, S., Gaubert, S., Han, L.: Perron\u2013Frobenius theorem for nonnegative multilinear forms and extensions. Linear Algebra Appl. 438, 738\u2013749 (2013)","journal-title":"Linear Algebra Appl."},{"key":"869_CR7","doi-asserted-by":"crossref","first-page":"1107","DOI":"10.1287\/opre.33.5.1107","volume":"33","author":"WK Grassmann","year":"1985","unstructured":"Grassmann, W.K., Taksar, M.J., Heyman, D.P.: Regenerative analysis and steady-state distributions for Markov chains. Oper. Res. 33, 1107\u20131116 (1985)","journal-title":"Oper. Res."},{"key":"869_CR8","unstructured":"Hu, S., Huang, Z.-H., Qi, L.: Finding the spectral radius of a nonnegative tensor. arXiv:1111.2138v1 (2011)"},{"key":"869_CR9","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/s10878-013-9596-x","volume":"29","author":"S Hu","year":"2015","unstructured":"Hu, S., Qi, L.: The Laplacian of a uniform hypergraph. J. Comb. Optim. 29, 331\u2013366 (2015)","journal-title":"J. Comb. Optim."},{"key":"869_CR10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.laa.2014.11.020","volume":"469","author":"S Hu","year":"2015","unstructured":"Hu, S., Qi, L., Xie, J.: The largest Laplacian and signless Laplacian $$H$$ H -eigenvalues of a uniform hypergraph. Linear Algebra Appl. 469, 1\u201327 (2015)","journal-title":"Linear Algebra Appl."},{"key":"869_CR11","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1007\/s00211-014-0677-2","volume":"130","author":"Z Jia","year":"2015","unstructured":"Jia, Z., Lin, W.-W., Liu, C.-S.: A positivity preserving inexact Noda iteration for computing the smallest eigenpair of a large irreducible $$M$$ M -matrix. Numer. Math. 130, 645\u2013679 (2015)","journal-title":"Numer. Math."},{"key":"869_CR12","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611970944","volume-title":"Iterative Methods for Linear and Nonlinear Equations","author":"CT Kelley","year":"1995","unstructured":"Kelley, C.T.: Iterative Methods for Linear and Nonlinear Equations. SIAM, Philadelphia, PA (1995)"},{"key":"869_CR13","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1137\/07070111X","volume":"51","author":"TG Kolda","year":"2009","unstructured":"Kolda, T.G., Bader, B.W.: Tensor decompositions and applications. SIAM Rev. 51, 455\u2013500 (2009)","journal-title":"SIAM Rev."},{"key":"869_CR14","unstructured":"Liu, C.-S., Guo, C.-H., Lin, W.-W.: A positivity preserving inverse iteration for finding the Perron pair of an irreducible nonnegative third order tensor. SIAM J. Matrix Anal. Appl. 37, 911\u2013932 (2016)"},{"key":"869_CR15","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1016\/j.cam.2010.06.002","volume":"235","author":"Y Liu","year":"2010","unstructured":"Liu, Y., Zhou, G., Ibrahim, N.F.: An always convergent algorithm for the largest eigenvalue of an irreducible nonnegative tensor. J. Comput. Appl. Math. 235, 286\u2013292 (2010)","journal-title":"J. Comput. Appl. Math."},{"key":"869_CR16","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1007\/s10898-014-0209-8","volume":"61","author":"Q Ni","year":"2015","unstructured":"Ni, Q., Qi, L.: A quadratically convergent algorithm for finding the largest eigenvalue of a nonnegative homogeneous polynomial map. J. Global Optim. 61, 627\u2013641 (2015)","journal-title":"J. Global Optim."},{"key":"869_CR17","doi-asserted-by":"crossref","first-page":"1090","DOI":"10.1137\/09074838X","volume":"31","author":"M Ng","year":"2009","unstructured":"Ng, M., Qi, L., Zhou, G.: Finding the largest eigenvalue of a nonnegative tensor. SIAM J. Matrix Anal. Appl. 31, 1090\u20131099 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"869_CR18","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1007\/BF01436087","volume":"17","author":"T Noda","year":"1971","unstructured":"Noda, T.: Note on the computation of the maximal eigenvalue of a non-negative irreducible matrix. Numer. Math. 17, 382\u2013386 (1971)","journal-title":"Numer. Math."},{"key":"869_CR19","first-page":"421","volume":"4","author":"KJ Pearson","year":"2010","unstructured":"Pearson, K.J.: Essentially positive tensors. Int. J. Algebra 4, 421\u2013427 (2010)","journal-title":"Int. J. Algebra"},{"key":"869_CR20","doi-asserted-by":"crossref","first-page":"528","DOI":"10.1111\/j.2517-6161.1985.tb01383.x","volume":"47","author":"AE Raftery","year":"1985","unstructured":"Raftery, A.E.: A model of high-order Markov chains. J. R. Stat. Soc. Ser. B 47, 528\u2013539 (1985)","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"869_CR21","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05156-2","volume-title":"Matrix Iterative Analysis","author":"RS Varga","year":"2000","unstructured":"Varga, R.S.: Matrix Iterative Analysis. Springer, Berlin (2000)"},{"key":"869_CR22","unstructured":"Yang, Y., Yang, Q.: On some properties of nonnegative weakly irreducible tensors. arXiv:1111.0713v2 (2011)"},{"key":"869_CR23","doi-asserted-by":"crossref","first-page":"2517","DOI":"10.1137\/090778766","volume":"31","author":"Y Yang","year":"2010","unstructured":"Yang, Y., Yang, Q.: Further results for Perron\u2013Frobenius Theorem for nonnegative tensors. SIAM. J. Matrix Anal. Appl. 31, 2517\u20132530 (2010)","journal-title":"SIAM. J. Matrix Anal. Appl."},{"key":"869_CR24","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1002\/nla.822","volume":"19","author":"L Zhang","year":"2012","unstructured":"Zhang, L., Qi, L.: Linear convergence of an algorithm for computing the largest eigenvalue of a nonnegative tensor. Numer. Linear Algebra Appl. 19, 830\u2013841 (2012)","journal-title":"Numer. Linear Algebra Appl."},{"key":"869_CR25","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1137\/130915339","volume":"35","author":"L Zhang","year":"2014","unstructured":"Zhang, L., Qi, L., Zhou, G.: $$M$$ M -tensors and some applications. SIAM J. Matrix Anal. Appl. 35, 437\u2013452 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-017-0869-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-017-0869-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-017-0869-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,22]],"date-time":"2024-06-22T16:33:15Z","timestamp":1719073995000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-017-0869-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,22]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2017,9]]}},"alternative-id":["869"],"URL":"https:\/\/doi.org\/10.1007\/s00211-017-0869-7","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,2,22]]}}}