{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,31]],"date-time":"2025-10-31T08:00:03Z","timestamp":1761897603062,"version":"3.37.3"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"7","license":[{"start":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T00:00:00Z","timestamp":1630972800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T00:00:00Z","timestamp":1630972800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100016883","name":"Funda\u00e7\u00e3o Getulio Vargas","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100016883","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003593","name":"CNPq","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003593","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s40314-021-01630-3","type":"journal-article","created":{"date-parts":[[2021,9,7]],"date-time":"2021-09-07T02:02:20Z","timestamp":1630980140000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Spectral residual method for nonlinear equations on Riemannian manifolds"],"prefix":"10.1007","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9139-0881","authenticated-orcid":false,"given":"Harry","family":"Oviedo","sequence":"first","affiliation":[]},{"given":"Hugo","family":"Lara","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,9,7]]},"reference":[{"key":"1630_CR1","doi-asserted-by":"crossref","unstructured":"Absil P-A, Gallivan KA (2006) Joint diagonalization on the oblique manifold for independent component analysis. In: 2006 IEEE international conference on acoustics speech and signal processing proceedings, vol\u00a05, pp V\u2013V. IEEE","DOI":"10.1109\/ICASSP.2006.1661433"},{"key":"1630_CR2","volume-title":"Optimization algorithms on matrix manifolds","author":"P-A Absil","year":"2009","unstructured":"Absil P-A, Mahony R, Sepulchre R (2009) Optimization algorithms on matrix manifolds. Princeton University Press, Princeton"},{"issue":"3","key":"1630_CR3","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1093\/imanum\/22.3.359","volume":"22","author":"RL Adler","year":"2002","unstructured":"Adler RL, Dedieu J-P, Margulies JY, Martens M, Shub M (2002) Newton\u2019s method on Riemannian manifolds and a geometric model for the human spine. IMA J Numer Anal 22(3):359\u2013390","journal-title":"IMA J Numer Anal"},{"issue":"1","key":"1630_CR4","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1093\/imanum\/8.1.141","volume":"8","author":"J Barzilai","year":"1988","unstructured":"Barzilai J, Borwein JM (1988) Two-point step size gradient methods. IMA J Numer Anal 8(1):141\u2013148","journal-title":"IMA J Numer Anal"},{"issue":"1","key":"1630_CR5","first-page":"1455","volume":"15","author":"N Boumal","year":"2014","unstructured":"Boumal N, Bamdev M, Absil P-A, Sepulchre R (2014) Manopt, a matlab toolbox for optimization on manifolds. J Mach Learn Res 15(1):1455\u20131459","journal-title":"J Mach Learn Res"},{"key":"1630_CR6","doi-asserted-by":"publisher","first-page":"42","DOI":"10.1016\/j.aml.2017.10.009","volume":"78","author":"P Breiding","year":"2018","unstructured":"Breiding P, Vannieuwenhoven N (2018) Convergence analysis of Riemannian Gauss-Newton methods and its connection with the geometric condition number. Appl Math Lett 78:42\u201350","journal-title":"Appl Math Lett"},{"issue":"3","key":"1630_CR7","doi-asserted-by":"publisher","first-page":"3118","DOI":"10.1007\/s40314-017-0501-6","volume":"37","author":"OSD Cedeno","year":"2018","unstructured":"Cedeno OSD, Leon HFO (2018) Projected nonmonotone search methods for optimization with orthogonality constraints. Comput Appl Math 37(3):3118\u20133144","journal-title":"Comput Appl Math"},{"issue":"1","key":"1630_CR8","first-page":"1","volume":"38","author":"TA Davis","year":"2011","unstructured":"Davis TA, Hu Y (2011) The university of florida sparse matrix collection. ACM Trans Math Softw (TOMS) 38(1):1","journal-title":"ACM Trans Math Softw (TOMS)"},{"issue":"2","key":"1630_CR9","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/s101070100263","volume":"91","author":"ED Dolan","year":"2002","unstructured":"Dolan ED, Mor\u00e9 JJ (2002) Benchmarking optimization software with performance profiles. Math Program 91(2):201\u2013213","journal-title":"Math Program"},{"issue":"2","key":"1630_CR10","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0895479895290954","volume":"20","author":"A Edelman","year":"1998","unstructured":"Edelman A, Arias TA, Smith ST (1998) The geometry of algorithms with orthogonality constraints. SIAM J Matrix Anal Appl 20(2):303\u2013353","journal-title":"SIAM J Matrix Anal Appl"},{"issue":"4","key":"1630_CR11","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1137\/0723046","volume":"23","author":"L Grippo","year":"1986","unstructured":"Grippo L, Lampariello F, Lucidi S (1986) A nonmonotone line search technique for newton\u2019s method. SIAM J Numer Anal 23(4):707\u2013716","journal-title":"SIAM J Numer Anal"},{"issue":"1","key":"1630_CR12","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1093\/imanum\/drx015","volume":"38","author":"B Iannazzo","year":"2018","unstructured":"Iannazzo B, Porcelli M (2018) The Riemannian Barzilai-Borwein method with nonmonotone line search and the matrix geometric mean computation. IMA J Numer Anal 38(1):495\u2013517","journal-title":"IMA J Numer Anal"},{"issue":"3","key":"1630_CR13","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1093\/imanum\/23.3.395","volume":"23","author":"D Jean-Pierre","year":"2003","unstructured":"Jean-Pierre D, Pierre P, Gregorio M (2003) Newton\u2019s method on Riemannian manifolds: covariant alpha theory. IMA J Numer Anal 23(3):395\u2013419","journal-title":"IMA J Numer Anal"},{"issue":"3","key":"1630_CR14","doi-asserted-by":"publisher","first-page":"565","DOI":"10.1002\/nla.743","volume":"18","author":"E Kokiopoulou","year":"2011","unstructured":"Kokiopoulou E, Chen J, Saad Y (2011) Trace optimization and eigenproblems in dimension reduction methods. Numer Linear Algebra Appl 18(3):565\u2013602","journal-title":"Numer Linear Algebra Appl"},{"issue":"5","key":"1630_CR15","doi-asserted-by":"publisher","first-page":"583","DOI":"10.1080\/10556780310001610493","volume":"18","author":"W La-Cruz","year":"2003","unstructured":"La-Cruz W, Raydan M (2003) Nonmonotone spectral methods for large-scale nonlinear systems. Optim Methods Softw 18(5):583\u2013599","journal-title":"Optim Methods Softw"},{"issue":"11","key":"1630_CR16","doi-asserted-by":"publisher","first-page":"1465","DOI":"10.1360\/04ys0147","volume":"48","author":"C Li","year":"2005","unstructured":"Li C, Wang J (2005) Convergence of the newton method and uniqueness of zeros of vector fields on Riemannian manifolds. Sci China Ser A Math 48(11):1465\u20131478","journal-title":"Sci China Ser A Math"},{"issue":"3","key":"1630_CR17","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1109\/78.984753","volume":"50","author":"JH Manton","year":"2002","unstructured":"Manton JH (2002) Optimization algorithms exploiting unitary constraints. IEEE Trans Signal Process 50(3):635\u2013650","journal-title":"IEEE Trans Signal Process"},{"key":"1630_CR18","doi-asserted-by":"publisher","DOI":"10.1017\/9781108555586","volume-title":"Electronic structure: basic theory and practical methods","author":"RM Martin","year":"2020","unstructured":"Martin RM (2020) Electronic structure: basic theory and practical methods. Cambridge University Press, Cambridge"},{"issue":"01","key":"1630_CR19","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1142\/S0129065789000475","volume":"1","author":"E Oja","year":"1989","unstructured":"Oja E (1989) Neural networks, principal components, and subspaces. Int J Neural Syst 1(01):61\u201368","journal-title":"Int J Neural Syst"},{"key":"1630_CR20","unstructured":"Oviedo H (2021a) Global convergence of riemannian line search methods with a zhang\u2013hager\u2013type condition. Preprint in Optimization\u2013Online. http:\/\/www.optimization-online.org\/DB_HTML\/2021\/03\/8297.html"},{"key":"1630_CR21","doi-asserted-by":"crossref","unstructured":"Oviedo H (2021b) Implicit steepest descent algorithm for optimization with orthogonality constraints. Preprint in Optimization\u2013Online. http:\/\/www.optimization-online.org\/DB_HTML\/2020\/03\/7682.html","DOI":"10.1007\/s11590-021-01801-5"},{"key":"1630_CR22","unstructured":"Oviedo H (2021c) Proximal point algorithm on the stiefel manifold. Preprint in Optimization-Online. http:\/\/www.optimization-online.org\/DB_FILE\/2021\/05\/8401.pdf"},{"key":"1630_CR23","first-page":"239","volume-title":"A scaled gradient projection method for minimization over the stiefel manifold","author":"H Oviedo","year":"2019","unstructured":"Oviedo H, Dalmau O (2019) A scaled gradient projection method for minimization over the stiefel manifold. Springer, New York, pp 239\u2013250"},{"issue":"2","key":"1630_CR24","doi-asserted-by":"publisher","first-page":"437","DOI":"10.1080\/10556788.2017.1415337","volume":"34","author":"H Oviedo","year":"2019","unstructured":"Oviedo H, Lara H, Dalmau O (2019) A non-monotone linear search algorithm with mixed direction on stiefel manifold. Optim Methods Softw 34(2):437\u2013457","journal-title":"Optim Methods Softw"},{"issue":"3","key":"1630_CR25","doi-asserted-by":"publisher","first-page":"1107","DOI":"10.1007\/s11075-020-01001-9","volume":"87","author":"H Oviedo","year":"2021","unstructured":"Oviedo H, Dalmau O, Lara H (2021) Two adaptive scaled gradient projection methods for stiefel manifold constrained optimization. Numer Algorithms 87(3):1107\u20131127","journal-title":"Numer Algorithms"},{"key":"1630_CR26","unstructured":"Oviedo H, Guerrero S (2021) Solving weighted orthogonal procrustes problems via a projected gradient method. Preprint in Optimization-Online. http:\/\/www.optimization-online.org\/DB_HTML\/2021\/05\/8375.html"},{"key":"1630_CR27","unstructured":"Oviedo H, Herrera R (2021) A efficient retraction mapping for the symplectic stiefel manifold. Preprint in Optimization-Online. http:\/\/www.optimization-online.org\/DB_HTML\/2021\/07\/8478.html"},{"issue":"3","key":"1630_CR28","doi-asserted-by":"publisher","first-page":"321","DOI":"10.1093\/imanum\/13.3.321","volume":"13","author":"M Raydan","year":"1993","unstructured":"Raydan M (1993) On the barzilai and borwein choice of steplength for the gradient method. IMA J Numer Anal 13(3):321\u2013326","journal-title":"IMA J Numer Anal"},{"issue":"1","key":"1630_CR29","doi-asserted-by":"publisher","first-page":"26","DOI":"10.1137\/S1052623494266365","volume":"7","author":"M Raydan","year":"1997","unstructured":"Raydan M (1997) The barzilai and borwein gradient method for the large scale unconstrained minimization problem. SIAM J Optim 7(1):26\u201333","journal-title":"SIAM J Optim"},{"issue":"2","key":"1630_CR30","doi-asserted-by":"publisher","first-page":"596","DOI":"10.1137\/11082885X","volume":"22","author":"W Ring","year":"2012","unstructured":"Ring W, Wirth B (2012) Optimization methods on riemannian manifolds and their application to shape space. SIAM J Optim 22(2):596\u2013627","journal-title":"SIAM J Optim"},{"issue":"1","key":"1630_CR31","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1137\/060651653","volume":"52","author":"Y Saad","year":"2010","unstructured":"Saad Y, Chelikowsky JR, Shontz SM (2010) Numerical methods for electronic structure calculations of materials. SIAM Rev 52(1):3\u201354","journal-title":"SIAM Rev"},{"key":"1630_CR32","unstructured":"Sato H (2014) Riemannian Newton\u2019s method for joint diagonalization on the stiefel manifold with application to ica. arXiv preprint arXiv:1403.8064"},{"issue":"4","key":"1630_CR33","doi-asserted-by":"publisher","first-page":"1011","DOI":"10.1080\/02331934.2013.836650","volume":"64","author":"H Sato","year":"2015","unstructured":"Sato H, Iwai T (2015) A new, globally convergent Riemannian conjugate gradient method. Optimization 64(4):1011\u20131031","journal-title":"Optimization"},{"key":"1630_CR34","unstructured":"Son NT, Absil P-A, Gao B, Stykel T (2021) Symplectic eigenvalue problem via trace minimization and Riemannian optimization. arXiv preprint arXiv:2101.02618,"},{"key":"1630_CR35","doi-asserted-by":"crossref","unstructured":"Turaga P, Veeraraghavan A, Chellappa R (2008) Statistical analysis on Stiefel and Grassmann manifolds with applications in computer vision. In: 2008 IEEE conference on computer vision and pattern recognition, pp 1\u20138. IEEE","DOI":"10.1109\/CVPR.2008.4587733"},{"issue":"3","key":"1630_CR36","doi-asserted-by":"publisher","first-page":"1175","DOI":"10.1007\/s10915-015-0061-0","volume":"66","author":"Z Wen","year":"2016","unstructured":"Wen Z, Yang C, Liu X, Zhang Y (2016) Trace-penalty minimization for large-scale eigenspace computation. J Sci Comput 66(3):1175\u20131203","journal-title":"J Sci Comput"},{"issue":"1","key":"1630_CR37","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1007\/s11075-020-00891-z","volume":"86","author":"T-T Yao","year":"2021","unstructured":"Yao T-T, Zhao Z, Bai Z-J, JinX-Q (2021) A Riemannian derivative-free polak-ribi\u00e9re-polyak method for tangent vector field. Numer Algorithms 86(1):325\u2013355","journal-title":"Numer Algorithms"},{"issue":"4","key":"1630_CR38","doi-asserted-by":"publisher","first-page":"1043","DOI":"10.1137\/S1052623403428208","volume":"14","author":"H Zhang","year":"2004","unstructured":"Zhang H, Hager WW (2004) A nonmonotone line search technique and its application to unconstrained optimization. SIAM J Optim 14(4):1043\u20131056","journal-title":"SIAM J Optim"},{"issue":"1","key":"1630_CR39","first-page":"3101","volume":"19","author":"T Zhang","year":"2018","unstructured":"Zhang T, Yang Y (2018) Robust pca by manifold optimization. J Mach Learn Res 19(1):3101\u20133139","journal-title":"J Mach Learn Res"},{"issue":"3","key":"1630_CR40","doi-asserted-by":"publisher","first-page":"C265","DOI":"10.1137\/130932934","volume":"36","author":"X Zhang","year":"2014","unstructured":"Zhang X, Zhu J, Wen Z, Zhou A (2014) Gradient type optimization methods for electronic structure calculations. SIAM J Sci Comput 36(3):C265\u2013C289","journal-title":"SIAM J Sci Comput"},{"issue":"1","key":"1630_CR41","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1007\/s10589-016-9883-4","volume":"67","author":"X Zhu","year":"2017","unstructured":"Zhu X (2017) A riemannian conjugate gradient method for optimization on the stiefel manifold. Comput Optim Appl 67(1):73\u2013110","journal-title":"Comput Optim Appl"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01630-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-021-01630-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-021-01630-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,7]],"date-time":"2024-09-07T22:32:44Z","timestamp":1725748364000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-021-01630-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,7]]},"references-count":41,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["1630"],"URL":"https:\/\/doi.org\/10.1007\/s40314-021-01630-3","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2021,9,7]]},"assertion":[{"value":"16 October 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 August 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 August 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 September 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"238"}}