{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,16]],"date-time":"2026-04-16T18:41:42Z","timestamp":1776364902517,"version":"3.51.2"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2015,11,2]],"date-time":"2015-11-02T00:00:00Z","timestamp":1446422400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Found Comput Math"],"published-print":{"date-parts":[[2017,4]]},"DOI":"10.1007\/s10208-015-9291-7","type":"journal-article","created":{"date-parts":[[2015,11,2]],"date-time":"2015-11-02T17:03:22Z","timestamp":1446483802000},"page":"423-465","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":42,"title":["Generating Polynomials and Symmetric Tensor Decompositions"],"prefix":"10.1007","volume":"17","author":[{"given":"Jiawang","family":"Nie","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,11,2]]},"reference":[{"key":"9291_CR1","first-page":"201","volume":"4","author":"J Alexander","year":"1995","unstructured":"J.\u00a0Alexander and A.\u00a0Hirschowitz. Polynomial interpolation in several variables. J. Algebraic Geom.\u00a0 4(1995), pp. 201-22.","journal-title":"J. Algebraic Geom."},{"key":"9291_CR2","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.1007\/s00209-011-0907-6","volume":"271","author":"E Balllico","year":"2012","unstructured":"E.\u00a0Balllico and A.\u00a0Bernardi. Decomposition of homogeneous polynomials with low rank. Math. Z. \u00a0 271, \u00a0 1141-1149, \u00a0 2012.","journal-title":"Math. Z."},{"key":"9291_CR3","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1016\/j.jsc.2010.08.001","volume":"46","author":"A Bernardi","year":"2011","unstructured":"A.\u00a0Bernardi, A.\u00a0Gimigliano and M.\u00a0Id\u00e0. Computing symmetric rank for symmetric tensors. Journal of Symbolic Computation \u00a0 46, (2011), 34-53.","journal-title":"Journal of Symbolic Computation"},{"issue":"11\u201312","key":"9291_CR4","doi-asserted-by":"crossref","first-page":"1851","DOI":"10.1016\/j.laa.2010.06.046","volume":"433","author":"J Brachat","year":"2010","unstructured":"J.\u00a0Brachat, P.\u00a0Comon, B.\u00a0Mourrain and E.\u00a0Tsigaridas. Symmetric tensor decomposition. Linear Algebra Appl. \u00a0 433, no. 11-12, 1851-1872, 2010.","journal-title":"Linear Algebra Appl."},{"key":"9291_CR5","doi-asserted-by":"crossref","unstructured":"W.\u00a0Buczy\u0144ska and J.\u00a0Buczy\u0144ski. Secant varieties to high degree Veronese reembeddings, catalecticant matrices and smoothable Gorenstein schemes. Journal of Algebraic Geometry, to appear. arXiv:1012.3563","DOI":"10.1090\/S1056-3911-2013-00595-0"},{"issue":"1","key":"9291_CR6","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1007\/s10208-010-9077-x","volume":"11","author":"G Comas","year":"2011","unstructured":"G.\u00a0Comas and M.\u00a0Seiguer. On the rank of a binary form. Foundations of Computational Mathematics, Vol.\u00a011, No.\u00a01, pp. 65-78, 2011.","journal-title":"Foundations of Computational Mathematics"},{"key":"9291_CR7","unstructured":"P.\u00a0Comon. Tensor decompositions - state of the art and applications. Keynote address in IMA Conf. in signal processing, Warwick, UK, 2000."},{"issue":"3","key":"9291_CR8","doi-asserted-by":"crossref","first-page":"1254","DOI":"10.1137\/060661569","volume":"30","author":"P Comon","year":"2008","unstructured":"P. Comon, G. Golub, L.-H. Lim and B. Mourrain. Symmetric tensors and symmetric tensor rank. SIAM Journal on Matrix Analysis and Applications, 30, no. 3, 1254-1279, 2008.","journal-title":"SIAM Journal on Matrix Analysis and Applications"},{"issue":"2","key":"9291_CR9","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1016\/0165-1684(96)00079-5","volume":"53","author":"P Comon","year":"1996","unstructured":"P. Comon and B. Mourrain. Decomposition of quantics in sums of powers of linear forms. Signal Processing \u00a0 53(2), 93-107, 1996. Special issue on high-order statistics.","journal-title":"Signal Processing"},{"key":"9291_CR10","doi-asserted-by":"crossref","unstructured":"D.\u00a0Cox, J.\u00a0Little and D.\u00a0O\u2019Shea. Ideals, varieties, and algorithms: an introduction to computational algebraic geometry and commutative algebra, Springer, 2007.","DOI":"10.1007\/978-0-387-35651-8"},{"key":"9291_CR11","doi-asserted-by":"crossref","unstructured":"R.\u00a0M.\u00a0Corless, P.\u00a0M.\u00a0Gianni and B.\u00a0M.\u00a0Trager. A reordered Schur factorization method for zero-dimensional polynomial systems with multiple roots. Proc. ACM Int. Symp. Symbolic and Algebraic Computation, 133-140, Maui, Hawaii, 1997.","DOI":"10.1145\/258726.258767"},{"key":"9291_CR12","doi-asserted-by":"crossref","unstructured":"R. Curto and L. Fialkow. Solution of the truncated complex moment problem for flat data. Memoirs of the American Mathematical Society, 119(1996), No. 568, Amer. Math. Soc., Providence, RI, 1996.","DOI":"10.1090\/memo\/0568"},{"key":"9291_CR13","doi-asserted-by":"crossref","unstructured":"R. Curto and L. Fialkow. Flat extensions of positive moment matrices: recursively generated relations. Memoirs of the American Mathematical Society, no. 648, American Mathematical Society, Providence, 1998.","DOI":"10.1090\/memo\/0648"},{"key":"9291_CR14","first-page":"189","volume":"54","author":"R Curto","year":"2005","unstructured":"R. Curto and L. Fialkow. Truncated K-moment problems in several variables. Journal of Operator Theory, 54(2005), pp. 189-226.","journal-title":"Journal of Operator Theory"},{"key":"9291_CR15","volume-title":"Numerical methods for unconstrained optimization and nonlinear equations","author":"JE Dennis","year":"1983","unstructured":"J. E. Dennis and R. B. Schnabel. Numerical methods for unconstrained optimization and nonlinear equations, Prentice-Hall, Englewood Cliffs, NJ, 1983."},{"key":"9291_CR16","doi-asserted-by":"crossref","unstructured":"J.B.\u00a0Lasserre, M.\u00a0Laurent, B.\u00a0Mourrain, P.\u00a0Rostalski, and P.\u00a0Trebuchet. Moment matrices, border bases and real radical computation. J. Symbolic Computation\u00a0 51, pp. 63\u201385.","DOI":"10.1016\/j.jsc.2012.03.007"},{"key":"9291_CR17","doi-asserted-by":"crossref","unstructured":"J.\u00a0Harris. Algebraic geometry: a first course. Graduate Textbooks in Mathematics, Springer, 1992.","DOI":"10.1007\/978-1-4757-2189-8"},{"key":"9291_CR18","doi-asserted-by":"crossref","unstructured":"C.\u00a0Hillar and L.-H.\u00a0Lim. Most tensor problems are NP-hard. Journal of the ACM, 60 (2013), no. 6, Art. 45.","DOI":"10.1145\/2512329"},{"key":"9291_CR19","doi-asserted-by":"crossref","unstructured":"A.\u00a0Iarrobino and V.\u00a0Kanev. Power Sums, Gorenstein algebras, and determinantal varieties. Lecture Notes in Mathematics #1721, Springer, 1999.","DOI":"10.1007\/BFb0093426"},{"key":"9291_CR20","doi-asserted-by":"crossref","unstructured":"C. T. Kelley. Iterative methods for linear and nonlinear equations, Frontiers in Applied Mathematics 16, SIAM, Philadelphia, 1995.","DOI":"10.1137\/1.9781611970944"},{"key":"9291_CR21","doi-asserted-by":"crossref","unstructured":"J.M.\u00a0Landsberg. Tensors: geometry and applications. Graduate Studies in Mathematics, 128. American Mathematical Society, Providence, RI, 2012.","DOI":"10.1090\/gsm\/128"},{"key":"9291_CR22","volume-title":"Handbook of Linear Algebra","author":"L-H Lim","year":"2013","unstructured":"L.-H. Lim. Tensors and hypermatrices, in: L. Hogben (Ed.), Handbook of Linear Algebra, 2nd Ed., CRC Press, Boca Raton, FL, 2013.","edition":"2"},{"key":"9291_CR23","first-page":"105","volume-title":"Lecture Notes in Mathematics 630: Numerical Analysis","author":"JJ More","year":"1978","unstructured":"J. J. More. The Levenberg-Marquardt algorithm: implementation and theory, in: G. A. Watson, ed., Lecture Notes in Mathematics 630: Numerical Analysis, Springer-Verlag, Berlin, 1978, 105\u2013116."},{"key":"9291_CR24","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/j.jsc.2012.11.005","volume":"54","author":"L Oeding","year":"2013","unstructured":"L.\u00a0Oeding and G.\u00a0Ottaviani. Eigenvectors of tensors and algorithms for Waring decomposition. J. Symbolic Comput.\u00a0 54, 9-35, 2013.","journal-title":"J. Symbolic Comput."},{"key":"9291_CR25","volume-title":"Basic algebraic geometry 1: varieties in projective space","author":"I Shafarevich","year":"1994","unstructured":"I.\u00a0Shafarevich. Basic algebraic geometry\u00a01: varieties in projective space, 2nd edition, Springer, Berlin 1994.","edition":"2"},{"key":"9291_CR26","doi-asserted-by":"crossref","unstructured":"B. Sturmfels. Solving systems of polynomial equations. CBMS Regional Conference Series in Mathematics, 97. American Mathematical Society, Providence, RI, 2002.","DOI":"10.1090\/cbms\/097"},{"key":"9291_CR27","doi-asserted-by":"crossref","first-page":"15","DOI":"10.3934\/naco.2011.1.15","volume":"1","author":"YX Yuan","year":"2011","unstructured":"Y. X. Yuan. Recent advances in numerical methods for nonlinear equations and nonlinear least squares, Numerical Algebra Control and Optimization, 1 (2011), 15\u201334.","journal-title":"Numerical Algebra Control and Optimization"}],"container-title":["Foundations of Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-015-9291-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10208-015-9291-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-015-9291-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10208-015-9291-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,1]],"date-time":"2019-09-01T05:47:49Z","timestamp":1567316869000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10208-015-9291-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,11,2]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2017,4]]}},"alternative-id":["9291"],"URL":"https:\/\/doi.org\/10.1007\/s10208-015-9291-7","relation":{},"ISSN":["1615-3375","1615-3383"],"issn-type":[{"value":"1615-3375","type":"print"},{"value":"1615-3383","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,11,2]]}}}