{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T09:29:29Z","timestamp":1768728569714,"version":"3.49.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,4,24]],"date-time":"2009-04-24T00:00:00Z","timestamp":1240531200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Comput Optim Appl"],"published-print":{"date-parts":[[2010,6]]},"DOI":"10.1007\/s10589-009-9250-9","type":"journal-article","created":{"date-parts":[[2009,4,23]],"date-time":"2009-04-23T13:50:46Z","timestamp":1240494646000},"page":"217-227","source":"Crossref","is-referenced-by-count":4,"title":["Residual algorithm for large-scale positive definite generalized eigenvalue problems"],"prefix":"10.1007","volume":"46","author":[{"given":"Lenys","family":"Bello","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"William","family":"La\u00a0Cruz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcos","family":"Raydan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,4,24]]},"reference":[{"key":"9250_CR1","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1006\/jcph.1998.6064","volume":"146","author":"J. Baglama","year":"1998","unstructured":"Baglama, J., Calvetti, D., Reichel, L., Ruttan, A.: Computation of a few small eigenvalues of a large matrix with application to liquid crystal modeling. J. Comput. Phys. 146, 203\u2013226 (1998)","journal-title":"J. Comput. Phys."},{"key":"9250_CR2","unstructured":"Bello, L.: Gradiente espectral precondicionado sobre convexos y algunos casos de estudio. Doctoral Thesis, Universidad Central de Venezuela, Caracas, Venezuela (2007)"},{"key":"9250_CR3","first-page":"4","volume":"22","author":"L. Bello","year":"2005","unstructured":"Bello, L., Raydan, M.: Preconditioned spectral projected gradient method on convex sets. J. Comput. Math. 22, 4\u201349 (2005)","journal-title":"J. Comput. Math."},{"key":"9250_CR4","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1023\/A:1019928808826","volume":"23","author":"E.G. Birgin","year":"2002","unstructured":"Birgin, E.G., Mart\u00ednez, J.M.: Large-scale active-set box-constrained optimization methods with spectral projected gradients. Comput. Optim. Appl. 23, 101\u2013125 (2002)","journal-title":"Comput. Optim. Appl."},{"key":"9250_CR5","doi-asserted-by":"crossref","first-page":"1196","DOI":"10.1137\/S1052623497330963","volume":"10","author":"E.G. Birgin","year":"2000","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Nonmonotone spectral projected gradient methods on convex sets. SIAM J. Opt. 10, 1196\u20131211 (2000)","journal-title":"SIAM J. Opt."},{"key":"9250_CR6","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1145\/502800.502803","volume":"27","author":"E.G. Birgin","year":"2001","unstructured":"Birgin, E.G., Mart\u00ednez, J.M., Raydan, M.: Algorithm 813: SPG\u2014software for convex-constrained optimization. ACM Trans. Math. Softw. 27, 340\u2013349 (2001)","journal-title":"ACM Trans. Math. Softw."},{"key":"9250_CR7","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1007\/BF02162089","volume":"9","author":"W.W. Bradbury","year":"1966","unstructured":"Bradbury, W.W., Fletcher, R.: New iterative methods for solution of the eigenproblem. Numer. Math. 9, 259\u2013267 (1966)","journal-title":"Numer. Math."},{"key":"9250_CR8","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/BF02127702","volume":"6","author":"J.H. Bramble","year":"1996","unstructured":"Bramble, J.H., Pasciak, J.E., Knyazev, A.V.: A subspace preconditioning algorithm for eigenvector\/eigenvalue computation. Adv. Comput. Math. 6, 159\u2013189 (1996)","journal-title":"Adv. Comput. Math."},{"key":"9250_CR9","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/j.cma.2003.09.013","volume":"193","author":"A.P. Costa","year":"2004","unstructured":"Costa, A.P., Figueiredo, I.N., J\u00fadice, J., Martins, J.A.C.: The directional instability problem in systems with frictional contacts. Comput. Methods Appl. Mech. Eng. 193, 357\u2013384 (2004)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"9250_CR10","doi-asserted-by":"crossref","first-page":"986","DOI":"10.1137\/040613305","volume":"16","author":"Y.H. Dai","year":"2006","unstructured":"Dai, Y.H.: Fast algorithms for projection on an ellipsoid. SIAM J. Opt. 16, 986\u20131006 (2006)","journal-title":"SIAM J. Opt."},{"key":"9250_CR11","volume-title":"Numerical Linear Algebra and Applications","author":"B.N. Datta","year":"1995","unstructured":"Datta, B.N.: Numerical Linear Algebra and Applications. Brooks\/Cole, Pacific Grove (1995)"},{"key":"9250_CR12","volume-title":"Numerical Methods for Linear Control Systems Design and Analysis","author":"B.N. Datta","year":"2003","unstructured":"Datta, B.N.: Numerical Methods for Linear Control Systems Design and Analysis. Elsevier, Amsterdam (2003)"},{"key":"9250_CR13","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/62038.62043","volume":"15","author":"I. Duff","year":"1989","unstructured":"Duff, I., Grimes, R., Lewis, J.: Sparse matrix test problems. ACM Trans. Math. Softw. 15, 1\u201314 (1989)","journal-title":"ACM Trans. Math. Softw."},{"key":"9250_CR14","doi-asserted-by":"crossref","first-page":"45","DOI":"10.6028\/jres.047.008","volume":"47","author":"M.R. Hestenes","year":"1951","unstructured":"Hestenes, M.R., Karush, W.: A method of gradients for the calculation of the characteristic roots and vectors of a real symmetric matrix. J. Res. Nat. Bureau Stand. 47, 45\u201361 (1951)","journal-title":"J. Res. Nat. Bureau Stand."},{"key":"9250_CR15","volume-title":"Engineering Vibration","author":"D.J. Inman","year":"1994","unstructured":"Inman, D.J.: Engineering Vibration. Prentice-Hall, Englewood Cliffs (1994)"},{"key":"9250_CR16","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1007\/s10589-007-9017-0","volume":"37","author":"J.J. J\u00fadice","year":"2007","unstructured":"J\u00fadice, J.J., Ribeiro, I., Sherali, H.: The eigenvalue complementarity problem. Comput. Optim. Appl. 37, 139\u2013156 (2007)","journal-title":"Comput. Optim. Appl."},{"key":"9250_CR17","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1080\/10556780310001610493","volume":"18","author":"W. La Cruz","year":"2003","unstructured":"La Cruz, W., Raydan, M.: Nonmonotone spectral methods for large-scale nonlinear systems. Optim. Methods Softw. 18, 583\u2013599 (2003)","journal-title":"Optim. Methods Softw."},{"key":"9250_CR18","doi-asserted-by":"crossref","first-page":"1449","DOI":"10.1090\/S0025-5718-06-01840-0","volume":"75","author":"W. La Cruz","year":"2006","unstructured":"La Cruz, W., Mart\u00ednez, J.M., Raydan, M.: Spectral residual method without gradient information for solving large-scale nonlinear systems. Math. Comput. 75, 1449\u20131466 (2006)","journal-title":"Math. Comput."},{"key":"9250_CR19","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/S0022-0000(76)80031-1","volume":"13","author":"S.F. McCormick","year":"1976","unstructured":"McCormick, S.F.: Some convergence results on the method of gradients for Ax=\u03bb Bx. J. Comput. Syst. Sci. 13, 213\u2013222 (1976)","journal-title":"J. Comput. Syst. Sci."},{"key":"9250_CR20","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1002\/nla.272","volume":"9","author":"K. Neymeyr","year":"2002","unstructured":"Neymeyr, K.: A posteriori error estimation for elliptic eigenproblems. Numer. Linear Algebra Appl. 9, 263\u2013279 (2002)","journal-title":"Numer. Linear Algebra Appl."},{"key":"9250_CR21","doi-asserted-by":"crossref","first-page":"1849","DOI":"10.1090\/S0025-5718-03-01614-4","volume":"73","author":"M.G. Queiroz","year":"2004","unstructured":"Queiroz, M.G., J\u00fadice, J.J., Humes, C. Jr.: The symmetric eigenvalue complementarity problem. Math. Comput. 73, 1849\u20131863 (2004)","journal-title":"Math. Comput."},{"key":"9250_CR22","volume-title":"Numerical Methods for Large Eigenvalue Problems","author":"Y. Saad","year":"1992","unstructured":"Saad, Y.: Numerical Methods for Large Eigenvalue Problems. Manchester University Press, Manchester (1992)"},{"key":"9250_CR23","unstructured":"Tango project web page: http\/\/www.ime.usp.br\/~egbirgin\/tango"},{"key":"9250_CR24","first-page":"1","volume":"2","author":"Y. Zhou","year":"2000","unstructured":"Zhou, Y.: Eigenvalue computation from the optimization perspective: on Jacobi-Davidson, IIGD, RQI and Newton updates. Numer. Linear Algebra Appl. 2, 1\u20136 (2000)","journal-title":"Numer. Linear Algebra Appl."}],"container-title":["Computational Optimization and Applications"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9250-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10589-009-9250-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10589-009-9250-9","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,31]],"date-time":"2019-05-31T11:36:36Z","timestamp":1559302596000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10589-009-9250-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4,24]]},"references-count":24,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,6]]}},"alternative-id":["9250"],"URL":"https:\/\/doi.org\/10.1007\/s10589-009-9250-9","relation":{},"ISSN":["0926-6003","1573-2894"],"issn-type":[{"value":"0926-6003","type":"print"},{"value":"1573-2894","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4,24]]}}}