{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T10:39:11Z","timestamp":1778755151250,"version":"3.51.4"},"reference-count":20,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2020,8,8]],"date-time":"2020-08-08T00:00:00Z","timestamp":1596844800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,8,8]],"date-time":"2020-08-08T00:00:00Z","timestamp":1596844800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100010663","name":"H2020 European Research Council","doi-asserted-by":"publisher","award":["666981"],"award-info":[{"award-number":["666981"]}],"id":[{"id":"10.13039\/100010663","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001665","name":"Agence Nationale de la Recherche","doi-asserted-by":"publisher","award":["ANR-19-PI3A-0004"],"award-info":[{"award-number":["ANR-19-PI3A-0004"]}],"id":[{"id":"10.13039\/501100001665","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Math. Program."],"published-print":{"date-parts":[[2021,11]]},"DOI":"10.1007\/s10107-020-01549-3","type":"journal-article","created":{"date-parts":[[2020,8,8]],"date-time":"2020-08-08T13:02:34Z","timestamp":1596891754000},"page":"795-809","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Connecting optimization with spectral analysis of tri-diagonal matrices"],"prefix":"10.1007","volume":"190","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0860-9913","authenticated-orcid":false,"given":"Jean B.","family":"Lasserre","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2020,8,8]]},"reference":[{"key":"1549_CR1","first-page":"447","volume":"46","author":"JL Aurentz","year":"2017","unstructured":"Aurentz, J.L., Mach, T., Vandebril, R., Watkins, D.: Computing the eigenvalues of symmetric tri-diagonal matrices via Cayley transformation. Electron. Trans. Numer. Anal. 46, 447\u2013449 (2017)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"1549_CR2","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1090\/S0025-5718-1969-0238476-6","volume":"23","author":"P Businger","year":"1969","unstructured":"Businger, P.: Extremal properties of balanced tri-diagonal matrices. Math. Comput. 23, 193\u2013195 (1969)","journal-title":"Math. Comput."},{"key":"1549_CR3","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1007\/s10107-016-1043-1","volume":"162","author":"de Klerk","year":"2017","unstructured":"de Klerk, Laurent, M., Sun Z: Convergence analysis for Lasserre\u2019s measure-based hierarchy of upper bounds for polynomial optimization. Math. Prog. Ser. A 162, 363\u2013392 (2017)","journal-title":"Math. Prog. Ser. A"},{"key":"1549_CR4","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1137\/16M1065264","volume":"27","author":"de Klerk","year":"2017","unstructured":"de Klerk, Laurent, M., Hess R: Improved convergence rates for Lasserre-type hierarchies of upper bounds for box-constrained polynomial optimization. SIAM J. Optim. 27, 347\u2013367 (2017)","journal-title":"SIAM J. Optim."},{"key":"1549_CR5","doi-asserted-by":"publisher","first-page":"1317","DOI":"10.1287\/moor.2017.0906","volume":"43","author":"E de Klerk","year":"2018","unstructured":"de Klerk, E., Laurent, M.: Comparison of Lasserre\u2019s measure-based bounds for polynomial optimization to bounds obtained by simulated annealing. Math. Oper. Res. 43, 1317\u20131325 (2018)","journal-title":"Math. Oper. Res."},{"key":"1549_CR6","doi-asserted-by":"crossref","unstructured":"de Klerk, E., Laurent, M.: Convergence analysis of a Lasserre hierarchy of upper bounds for polynomial optimization on the sphere. Math. Program (2020) (to appear). arXiv:1904.08828 (2019)","DOI":"10.1007\/s10107-019-01465-1"},{"issue":"1","key":"1549_CR7","doi-asserted-by":"publisher","first-page":"86","DOI":"10.1287\/moor.2018.0983","volume":"45","author":"E de Klerk","year":"2019","unstructured":"de Klerk, E., Laurent, M.: Worst-case examples for Lasserre\u2019s measure-based hierarchy for polynomial optimization on the hypercube. Math. Oper. Res. 45(1), 86\u201398 (2019)","journal-title":"Math. Oper. Res."},{"key":"1549_CR8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511565717","volume-title":"Orthogonal Polynomials of Several Variables","author":"C Dunkl","year":"2001","unstructured":"Dunkl, C., Xu, Y.: Orthogonal Polynomials of Several Variables. Cambridge University Press, Cambridge (2001)"},{"key":"1549_CR9","volume-title":"Numerical Linear Algebra with Applications: Using MATLAB","author":"W Ford","year":"2015","unstructured":"Ford, W.: Numerical Linear Algebra with Applications: Using MATLAB. Academic Press, Amsterdam (2015)"},{"key":"1549_CR10","unstructured":"Kahan, W.: When to neglect off-diagonal elements of symmetric tri-diagonal matrices. Technical report. Stanford University, Stanford (1966)"},{"key":"1549_CR11","first-page":"345","volume":"197","author":"E Kili\u00e7","year":"2008","unstructured":"Kili\u00e7, E.: Explicit formula for the inverse of a tridiagonal matrix by backward continued fractions. Appl. Math. Comput. 197, 345\u2013357 (2008)","journal-title":"Appl. Math. Comput."},{"key":"1549_CR12","doi-asserted-by":"publisher","DOI":"10.1142\/p665","volume-title":"Moments, Positive Polynomials and Their Applications","author":"JB Lasserre","year":"2009","unstructured":"Lasserre, J.B.: Moments, Positive Polynomials and Their Applications. Imperial College Press, London (2009)"},{"key":"1549_CR13","doi-asserted-by":"publisher","first-page":"3375","DOI":"10.1090\/S0002-9939-2011-10865-7","volume":"139","author":"JB Lasserre","year":"2011","unstructured":"Lasserre, J.B.: Bounding the support of a measure from its marginal moments. Proc. Am. Math. Soc. 139, 3375\u20133382 (2011)","journal-title":"Proc. Am. Math. Soc."},{"key":"1549_CR14","doi-asserted-by":"publisher","first-page":"864","DOI":"10.1137\/100806990","volume":"21","author":"JB Lasserre","year":"2011","unstructured":"Lasserre, J.B.: A new look at nonnegativity on closed sets and polynomial optimization. SIAM J. Optim. 21, 864\u2013885 (2011)","journal-title":"SIAM J. Optim."},{"key":"1549_CR15","unstructured":"Laurent, M., Slot, L.: Near-optimal analysis of univariate moment bounds for polynomial optimization. arXiv:2001.11289 (2020)"},{"key":"1549_CR16","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/S0024-3795(00)00262-7","volume":"325","author":"RK Mallik","year":"2001","unstructured":"Mallik, R.K.: The inverse of a tridiagonal matrix. Linear Algorithm Appl. 325, 109\u2013139 (2001)","journal-title":"Linear Algorithm Appl."},{"key":"1549_CR17","series-title":"Nato ASI Series","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-0501-6","volume-title":"Orthogonal Polynomials: Theory and Practice","author":"P Nevai","year":"1990","unstructured":"Nevai, P.: Orthogonal Polynomials: Theory and Practice. Nato ASI Series. Kluwer Academic Publishers, Dordrecht (1990)"},{"key":"1549_CR18","unstructured":"Osipov, A.: Evaluation of small elements of the eigenvectors of certain symmetric tridiagonal matrices with high relative accuracy. Research Report YALEU\/DCS\/TR-1460. Yale University (2012)"},{"key":"1549_CR19","volume-title":"Matrix Algorithms in MATLAB","author":"OU Routh","year":"2016","unstructured":"Routh, O.U.: Matrix Algorithms in MATLAB. Academic Press, Amsterdam (2016)"},{"key":"1549_CR20","doi-asserted-by":"crossref","unstructured":"Slot, L., Laurent, M.: Improved convergence analysis of Lasserre\u2019s measure-based upper bounds for polynomial minimization on compact sets. Math. Program. (2020) (to appear). arXiv:1905.08142","DOI":"10.1007\/s10107-020-01468-3"}],"container-title":["Mathematical Programming"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-020-01549-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10107-020-01549-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10107-020-01549-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,10]],"date-time":"2021-10-10T02:53:06Z","timestamp":1633834386000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10107-020-01549-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,8]]},"references-count":20,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,11]]}},"alternative-id":["1549"],"URL":"https:\/\/doi.org\/10.1007\/s10107-020-01549-3","relation":{},"ISSN":["0025-5610","1436-4646"],"issn-type":[{"value":"0025-5610","type":"print"},{"value":"1436-4646","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,8]]},"assertion":[{"value":"19 August 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 July 2020","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 August 2020","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}