{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T12:07:37Z","timestamp":1759838857395,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,3,21]],"date-time":"2018-03-21T00:00:00Z","timestamp":1521590400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundations of China","doi-asserted-by":"crossref","award":["11771159"],"award-info":[{"award-number":["11771159"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2019,3]]},"DOI":"10.1007\/s11075-018-0512-4","type":"journal-article","created":{"date-parts":[[2018,3,21]],"date-time":"2018-03-21T04:44:11Z","timestamp":1521607451000},"page":"937-955","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Noda iterations for generalized eigenproblems following Perron-Frobenius theory"],"prefix":"10.1007","volume":"80","author":[{"given":"Xiao Shan","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seak-Weng","family":"Vong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wen","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hongguo","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,21]]},"reference":[{"key":"512_CR1","volume-title":"Templates for the solution of algebraic eigenvalue problems: a practical guide","author":"ZJ Bai","year":"2011","unstructured":"Bai, Z.J., Demmel, J., Dongarra, J., Ruhe, A., Van der Vorst, H.: Templates for the solution of algebraic eigenvalue problems: a practical guide. Philadelphia, SIAM (2011)"},{"key":"512_CR2","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1080\/03081089508818429","volume":"40","author":"RB Bapat","year":"1995","unstructured":"Bapat, R.B., OLesky, D.D., van den Driesseche, P.: Perron-frobenius theory for a generalized eigenproblem. Linear Multi. Algebra 40, 141\u2013152 (1995)","journal-title":"Linear Multi. Algebra"},{"key":"512_CR3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971262","volume-title":"Nonnegative matrices in the mathematical sciences, Classics Appl Math, vol. 9","author":"A Berman","year":"1994","unstructured":"Berman, A., Plemmons, R.J.: Nonnegative matrices in the mathematical sciences, Classics Appl Math, vol. 9. SIAM, Philadelphia (1994)"},{"key":"512_CR4","doi-asserted-by":"publisher","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."},{"issue":"2","key":"512_CR5","first-page":"269","volume":"23","author":"T Fujimoto","year":"1979","unstructured":"Fujimoto, T.: A generalization of the Frobenius theorem. Toyama University Econ. Rev. 23(2), 269\u2013274 (1979)","journal-title":"Toyama University Econ. Rev."},{"unstructured":"Golub, G.H., Van Loan, C.F.: Matrix computations, 4th edn. Johns Hopkins University Press, Baltimore (2013)","key":"512_CR6"},{"key":"512_CR7","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1016\/j.jcp.2014.06.012","volume":"274","author":"W Huang","year":"2014","unstructured":"Huang, W.: Sign-preserving of principal eigenfunctions in p1 finite element approximation of eigenvalue problems of second-order elliptic operators. J. Comput. Phys. 274, 230\u2013244 (2014)","journal-title":"J. Comput. Phys."},{"key":"512_CR8","doi-asserted-by":"publisher","first-page":"645","DOI":"10.1007\/s00211-014-0677-2","volume":"130","author":"ZX Jia","year":"2015","unstructured":"Jia, Z.X., Lin, W.-W., Liu, C.S.: A positivity preserving inexact Noda iteration for computing the smallest eigenpair of a large irreducible M-matrix. Numer. Math. 130, 645\u2013679 (2015)","journal-title":"Numer. Math."},{"issue":"4","key":"512_CR9","first-page":"645","volume":"130","author":"C-S Liu","year":"2015","unstructured":"Liu, C.-S.: An inexact Noda iteration for computing the smallest eigenpair of a large irreducible monotone matrix. Mathematics 130(4), 645\u2013679 (2015)","journal-title":"Mathematics"},{"key":"512_CR10","doi-asserted-by":"publisher","first-page":"911","DOI":"10.1137\/15M1040128","volume":"37","author":"C-S Liu","year":"2016","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 tensor. SIAM J. Matrix Anal. Appl. 37, 911\u2013932 (2016)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"512_CR11","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1016\/0304-4068(74)90010-X","volume":"1","author":"M Morishima","year":"1974","unstructured":"Morishima, M., Fujimoto, T.: The Frobenius theorem, its Solow Samuelson extension and the Kuhn-Tucker theorem. J. Math. Econ. 1, 199\u2013205 (1974)","journal-title":"J. Math. Econ."},{"key":"512_CR12","doi-asserted-by":"publisher","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":"512_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-05201-1","volume-title":"Essays on the theory of joint production","author":"LL Pasinetti","year":"1980","unstructured":"Pasinetti, L.L.: Essays on the theory of joint production. Macmillan Press, London (1980)"},{"key":"512_CR14","volume-title":"Production of commodities by means of commodities","author":"P Sraffa","year":"1960","unstructured":"Sraffa, P.: Production of commodities by means of commodities. Cambridge University Press, Cambridge (1960)"},{"key":"512_CR15","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718058","volume-title":"Matrix algorithms, Volume II: Eigensystems","author":"GW Stewart","year":"2001","unstructured":"Stewart, G.W.: Matrix algorithms, Volume II: Eigensystems. SIAM, Philadelphia (2001)"},{"key":"512_CR16","volume-title":"Matrix perturbation theory","author":"GW Steward","year":"1990","unstructured":"Steward, G.W., Sun, J.G.: Matrix perturbation theory. Academic Press, Boston (1990)"},{"key":"512_CR17","volume-title":"Matrix iterative analysis","author":"RS Varga","year":"1962","unstructured":"Varga, R.S.: Matrix iterative analysis. Springer, Berlin (1962)"},{"issue":"4","key":"512_CR18","doi-asserted-by":"publisher","first-page":"748","DOI":"10.1137\/S0895479894276953","volume":"17","author":"J Xue","year":"1996","unstructured":"Xue, J.: Computing the smallest eigenvalue of an M-matrix. SIAM J. Matrix Anal. Appl. 17(4), 748\u2013762 (1996)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"512_CR19","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/147","volume-title":"Matrix theory","author":"XZ Zhan","year":"2013","unstructured":"Zhan, X.Z.: Matrix theory. American Mathematical Society Providence, Rhode Island (2013)"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0512-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11075-018-0512-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-018-0512-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,20]],"date-time":"2019-03-20T20:09:00Z","timestamp":1553112540000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11075-018-0512-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,21]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2019,3]]}},"alternative-id":["512"],"URL":"https:\/\/doi.org\/10.1007\/s11075-018-0512-4","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2018,3,21]]},"assertion":[{"value":"23 December 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"11 March 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 March 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}