{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,11]],"date-time":"2026-01-11T00:51:20Z","timestamp":1768092680291,"version":"3.49.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,3,8]],"date-time":"2018-03-08T00:00:00Z","timestamp":1520467200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["11601261"],"award-info":[{"award-number":["11601261"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11571087,11771113"],"award-info":[{"award-number":["11571087,11771113"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2018,9]]},"DOI":"10.1007\/s10915-018-0689-7","type":"journal-article","created":{"date-parts":[[2018,3,8]],"date-time":"2018-03-08T10:43:23Z","timestamp":1520505803000},"page":"1718-1741","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":57,"title":["A Globally and Quadratically Convergent Algorithm for Solving Multilinear Systems with \n                \n                  \n                \n                $${{\\mathcal {M}}}$$\n                \n                  \n                    M\n                  \n                \n              -tensors"],"prefix":"10.1007","volume":"76","author":[{"given":"Hongjin","family":"He","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chen","family":"Ling","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liqun","family":"Qi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8811-885X","authenticated-orcid":false,"given":"Guanglu","family":"Zhou","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2018,3,8]]},"reference":[{"key":"689_CR1","unstructured":"Bader, B.W., Kolda, T.G., et\u00a0al.: MATLAB Tensor Toolbox Version 2.6. Available online (2015). \n                    http:\/\/www.sandia.gov\/~tgkolda\/TensorToolbox\/"},{"key":"689_CR2","doi-asserted-by":"publisher","first-page":"418","DOI":"10.1006\/jcph.2002.7176","volume":"182","author":"M Benzi","year":"2002","unstructured":"Benzi, M.: Preconditioning techniques for large linear systems: a survey. J. Comput. Phys. 182, 418\u2013477 (2002)","journal-title":"J. Comput. Phys."},{"key":"689_CR3","doi-asserted-by":"publisher","DOI":"10.1137\/1.9781611971262","volume-title":"Nonnegative Matrices in the Mathematical Sciences","author":"A Berman","year":"1994","unstructured":"Berman, A., Plemmons, R.: Nonnegative Matrices in the Mathematical Sciences. SIAM, Philadelphia (1994)"},{"issue":"2","key":"689_CR4","doi-asserted-by":"publisher","first-page":"542","DOI":"10.1137\/100804577","volume":"34","author":"M Brazell","year":"2013","unstructured":"Brazell, M., Li, N., Navasca, C., Tamon, C.: Solving multilinear systems via tensor inversion. SIAM J. Matrix Anal. Appl. 34(2), 542\u2013570 (2013)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"6","key":"689_CR5","doi-asserted-by":"publisher","first-page":"891","DOI":"10.1002\/nla.1902","volume":"20","author":"K Chang","year":"2013","unstructured":"Chang, K., Qi, L., Zhang, T.: A survey on the spectral theory of nonnegative tensors. Numer. Linear Algebra Appl. 20(6), 891\u2013912 (2013)","journal-title":"Numer. Linear Algebra Appl."},{"key":"689_CR6","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2125","author":"H Chen","year":"2017","unstructured":"Chen, H., Chen, Y., Li, G., Qi, L.: A semidefinite program approach for computing the maximum eigenvalue of a class of structured tensors and its applications in hypergraphs and copositivity test. Numer. Linear Algebra Appl. (2017). \n                    https:\/\/doi.org\/10.1002\/nla.2125","journal-title":"Numer. Linear Algebra Appl."},{"key":"689_CR7","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.: M-tensor and nonsingular M-tensors. Linear Algebra Appl. 439, 3264\u20133278 (2013)","journal-title":"Linear Algebra Appl."},{"key":"689_CR8","doi-asserted-by":"publisher","first-page":"689","DOI":"10.1007\/s10915-015-0156-7","volume":"68","author":"W Ding","year":"2016","unstructured":"Ding, W., Wei, Y.: Solving multilinear systems with M-tensors. J. Sci. Comput. 68, 689\u2013715 (2016)","journal-title":"J. Sci. Comput."},{"issue":"4","key":"689_CR9","doi-asserted-by":"publisher","first-page":"1150","DOI":"10.1137\/S0363012997322935","volume":"37","author":"F Facchinei","year":"1999","unstructured":"Facchinei, F., Kanzow, C.: Beyond monotonicity in regularization methods for nonlinear complementarity problems. SIAM J. Control Optim. 37(4), 1150\u20131161 (1999)","journal-title":"SIAM J. Control Optim."},{"key":"689_CR10","volume-title":"Finite-Dimensional Variational Inequalities and Complementarity Problems","author":"F Facchinei","year":"2003","unstructured":"Facchinei, F., Pang, J.: Finite-Dimensional Variational Inequalities and Complementarity Problems. Springer, New York (2003)"},{"key":"689_CR11","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.aml.2017.01.019","volume":"69","author":"L Han","year":"2017","unstructured":"Han, L.: A homotopy method for solving multilinear systems with M-tensors. Appl. Math. Lett. 69, 49\u201354 (2017)","journal-title":"Appl. Math. Lett."},{"issue":"4","key":"689_CR12","doi-asserted-by":"publisher","first-page":"1688","DOI":"10.1137\/090756843","volume":"31","author":"D Kressner","year":"2010","unstructured":"Kressner, D., Tobler, C.: Krylov subspace methods for linear systems with tensor product structure. SIAM J. Matrix Anal. Appl. 31(4), 1688\u20131714 (2010)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"689_CR13","doi-asserted-by":"publisher","DOI":"10.1002\/nla.2102","author":"D Li","year":"2017","unstructured":"Li, D., Xie, S., Xu, H.: Splitting methods for tensor equations. Numer. Linear Algebra Appl. (2017). \n                    https:\/\/doi.org\/10.1002\/nla.2102","journal-title":"Numer. Linear Algebra Appl."},{"key":"689_CR14","doi-asserted-by":"publisher","first-page":"649","DOI":"10.1007\/s11464-014-0377-3","volume":"10","author":"X Li","year":"2015","unstructured":"Li, X., Ng, M.: Solving sparse non-negative tensor equations: algorithms and applications. Front. Math. China 10, 649\u2013680 (2015)","journal-title":"Front. Math. China"},{"key":"689_CR15","doi-asserted-by":"publisher","first-page":"2317","DOI":"10.1063\/1.527764","volume":"28","author":"Y Matsuno","year":"1987","unstructured":"Matsuno, Y.: Exact solutions for the nonlinear Klein\u2013Gordon and Liouville equations in four-dimensional Euclidean space. J. Math. Phys. 28, 2317\u20132322 (1987)","journal-title":"J. Math. Phys."},{"issue":"2","key":"689_CR16","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1137\/S1052623497324047","volume":"10","author":"HD Qi","year":"2000","unstructured":"Qi, H.D.: A regularized smoothing Newton method for box constrained variational inequality problems with \n                    \n                      \n                    \n                    $$P_0$$\n                    \n                      \n                        \n                          P\n                          0\n                        \n                      \n                    \n                  -functions. SIAM J. Optim. 10(2), 315\u2013330 (2000)","journal-title":"SIAM J. Optim."},{"issue":"6","key":"689_CR17","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.: Eigenvalues of a real supersymmetric tensor. J. Symbolic Comput. 40(6), 1302\u20131324 (2005)","journal-title":"J. Symbolic Comput."},{"key":"689_CR18","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.: Tensor Analysis: Spectral Theory and Special Tensors. SIAM, Philadelphia (2017)"},{"issue":"1","key":"689_CR19","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s101079900127","volume":"87","author":"L Qi","year":"2000","unstructured":"Qi, L., Sun, D., Zhou, G.: A new look at smoothing newton methods for nonlinear complementarity problems and box constrained variational inequalities. Math. Program. 87(1), 1\u201335 (2000)","journal-title":"Math. Program."},{"key":"689_CR20","unstructured":"Tobler, C.: Low-rank tensor methods for linear systems and eigenvalue problems. Ph.D. Thesis, Eidgenssische Technische Hochschule ETH Zrich, No. 20320 (2012)"},{"key":"689_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0024-3795(76)90037-9","volume":"13","author":"R Varga","year":"1976","unstructured":"Varga, R.: On recurring theorems on diagonal dominance. Linear Algebra Appl. 13, 1\u20139 (1976)","journal-title":"Linear Algebra Appl."},{"key":"689_CR22","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-017-0444-5","author":"Z Xie","year":"2017","unstructured":"Xie, Z., Jin, X., Wei, Y.: Tensor methods for solving symmetric M-tensor systems. J. Sci. Comput. (2017). \n                    https:\/\/doi.org\/10.1007\/s10915-017-0444-5","journal-title":"J. Sci. Comput."},{"issue":"2","key":"689_CR23","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.: \n                    \n                      \n                    \n                    $$M$$\n                    \n                      \n                        M\n                      \n                    \n                  -tensors and some applications. SIAM J. Matrix Anal. Appl. 35(2), 437\u2013452 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"689_CR24","volume-title":"Handbook of Differential Equations","author":"D Zwillinger","year":"1997","unstructured":"Zwillinger, D.: Handbook of Differential Equations, 3rd edn. Academic Press Inc., Boston (1997)","edition":"3"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-018-0689-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0689-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-018-0689-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T19:31:32Z","timestamp":1551987092000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-018-0689-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,8]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["689"],"URL":"https:\/\/doi.org\/10.1007\/s10915-018-0689-7","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,8]]},"assertion":[{"value":"15 October 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 February 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 February 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 March 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}