{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:14:52Z","timestamp":1740107692336,"version":"3.37.3"},"reference-count":44,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2018,7,25]],"date-time":"2018-07-25T00:00:00Z","timestamp":1532476800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2018,7,25]],"date-time":"2018-07-25T00:00:00Z","timestamp":1532476800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1358884","1358884"],"award-info":[{"award-number":["1358884","1358884"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["MTM-2015-65798-P"],"award-info":[{"award-number":["MTM-2015-65798-P"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"crossref","award":["MTM-2015-68805_REDT"],"award-info":[{"award-number":["MTM-2015-68805_REDT"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003329","name":"Ministerio de Econom\u00eda y Competitividad","doi-asserted-by":"publisher","award":["MTM-2015-65798-P"],"award-info":[{"award-number":["MTM-2015-65798-P"]}],"id":[{"id":"10.13039\/501100003329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Calcolo"],"published-print":{"date-parts":[[2018,9]]},"DOI":"10.1007\/s10092-018-0273-4","type":"journal-article","created":{"date-parts":[[2018,7,25]],"date-time":"2018-07-25T12:16:07Z","timestamp":1532520967000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A block-symmetric linearization of odd degree matrix polynomials with optimal eigenvalue condition number and backward error"],"prefix":"10.1007","volume":"55","author":[{"given":"M. I.","family":"Bueno","sequence":"first","affiliation":[]},{"given":"F. M.","family":"Dopico","sequence":"additional","affiliation":[]},{"given":"S.","family":"Furtado","sequence":"additional","affiliation":[]},{"given":"L.","family":"Medina","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,7,25]]},"reference":[{"key":"273_CR1","doi-asserted-by":"publisher","first-page":"2193","DOI":"10.1016\/j.laa.2011.04.020","volume":"435","author":"B Adhikari","year":"2011","unstructured":"Adhikari, B., Alam, R., Kressner, D.: Structured eigenvalue condition numbers and linearizations for matrix polynomials. Linear Algebra Appl. 435, 2193\u20132221 (2011)","journal-title":"Linear Algebra Appl."},{"key":"273_CR2","doi-asserted-by":"publisher","first-page":"3954","DOI":"10.1016\/j.laa.2010.08.035","volume":"436","author":"M Al-Ammari","year":"2012","unstructured":"Al-Ammari, M., Tisseur, F.: Hermitian matrix polynomials with real eigenvalues of definite type. Part I: classification. Linear Algebra Appl. 436, 3954\u20133973 (2012)","journal-title":"Linear Algebra Appl."},{"key":"273_CR3","doi-asserted-by":"publisher","first-page":"78","DOI":"10.13001\/1081-3810.1124","volume":"11","author":"EN Antoniou","year":"2004","unstructured":"Antoniou, E.N., Vologiannidis, S.: A new family of companion forms of polynomial matrices. Electron. J. Linear Algebra 11, 78\u201387 (2004)","journal-title":"Electron. J. Linear Algebra"},{"issue":"2","key":"273_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2427023.2427024","volume":"39","author":"Timo Betcke","year":"2013","unstructured":"Betcke, T., Higham, N. J., Mehrmann, V., Schr\u00f6der, C., Tisseur, F.: NLEVP: a collection of nonlinear eigenvalue problems. ACM Trans. Math. Softw. 39(2), 7:1\u20137:28 (2013)","journal-title":"ACM Transactions on Mathematical Software"},{"key":"273_CR5","doi-asserted-by":"publisher","first-page":"153","DOI":"10.1137\/S0895479803429788","volume":"27","author":"DA Bini","year":"2005","unstructured":"Bini, D.A., Gemignani, L., Tisseur, F.: The Ehrlich\u2013Aberth method for the nonsymmetric tridiagonal eigenvalue problem. SIAM J. Matrix Anal. Appl. 27, 153\u2013175 (2005)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR6","doi-asserted-by":"publisher","first-page":"1130","DOI":"10.1016\/j.laa.2013.02.024","volume":"439","author":"DA Bini","year":"2013","unstructured":"Bini, D.A., Noferini, V.: Solving polynomial eigenvalue problems by means of the Ehrlich\u2013Aberth method. Linear Algebra Appl. 439, 1130\u20131149 (2013)","journal-title":"Linear Algebra Appl."},{"issue":"3","key":"273_CR7","doi-asserted-by":"publisher","first-page":"900","DOI":"10.1137\/060675769","volume":"31","author":"S Bora","year":"2009","unstructured":"Bora, S.: Structured eigenvalue condition number and backward error of a class of polynomial eigenvalue problems. SIAM J. Matrix Anal. Appl. 31(3), 900\u2013917 (2009)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR8","unstructured":"Bueno, M. I., Martin, M., P\u00e9rez, J., Song, A., Viviano, I.: Explicit block-structures for block-symmetric Fiedler-like pencils. To appear in ELA"},{"key":"273_CR9","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1016\/j.laa.2016.12.035","volume":"519","author":"MI Bueno","year":"2017","unstructured":"Bueno, M.I., Breen, J., Ford, S., Furtado, S.: On the sign characteristic of Hermitian linearizations in $$\\mathbb{DL}(P)$$. Linear Algebra Appl. 519, 73\u2013101 (2017)","journal-title":"Linear Algebra Appl."},{"key":"273_CR10","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1016\/j.laa.2015.03.032","volume":"477","author":"MI Bueno","year":"2015","unstructured":"Bueno, M.I., Dopico, F.M., Furtado, S., Rychnovsky, M.: Large vector spaces of block-symmetric strong linearizations. Linear Algebra Appl. 477, 165\u2013210 (2015)","journal-title":"Linear Algebra Appl."},{"key":"273_CR11","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1137\/100816808","volume":"32","author":"MI Bueno","year":"2011","unstructured":"Bueno, M.I., De Ter\u00e1n, F., Dopico, F.M.: Recovery of eigenvectors and minimal bases of matrix polynomials from generalized Fiedler linearizations. SIAM J. Matrix. Anal. Appl. 32, 463\u2013483 (2011)","journal-title":"SIAM J. Matrix. Anal. Appl."},{"key":"273_CR12","doi-asserted-by":"publisher","first-page":"S385","DOI":"10.1137\/15M1022458","volume":"38","author":"C Campos","year":"2016","unstructured":"Campos, C., Rom\u00e1n, J.: Parallel Krylov solvers for the polynomial eigenvalue problem in SLEPc. SIAM J. Sci. Comput. 38, S385\u2013S411 (2016)","journal-title":"SIAM J. Sci. Comput."},{"key":"273_CR13","doi-asserted-by":"publisher","first-page":"264","DOI":"10.1016\/j.laa.2014.07.007","volume":"459","author":"F De Ter\u00e1n","year":"2014","unstructured":"De Ter\u00e1n, F., Dopico, F.M., Mackey, D.S.: Spectral equivalence of matrix polynomials and the Index Sum Theorem. Linear Algebra Appl. 459, 264\u2013333 (2014)","journal-title":"Linear Algebra Appl."},{"issue":"2","key":"273_CR14","doi-asserted-by":"publisher","first-page":"373","DOI":"10.1007\/s00211-018-0969-z","volume":"140","author":"Froil\u00e1n M. Dopico","year":"2018","unstructured":"Dopico, F. M., Lawrence, P., P\u00e9rez, J., Van Dooren, P.: Block Kronecker linearizations of matrix polynomials and their backward errors. To appear in Numerische Mathematik (2018). \n                    arXiv:1707.04843v1","journal-title":"Numerische Mathematik"},{"key":"273_CR15","doi-asserted-by":"crossref","unstructured":"Dopico, F. M., P\u00e9rez, J., Van Dooren, P.: Structured backward error analysis of linearized structured polynomial eigenvalue problems. To appear in Mathematics of Computation (2018). \n                    arXiv:1612.07011v1","DOI":"10.1090\/mcom\/3360"},{"key":"273_CR16","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1016\/j.laa.2017.03.017","volume":"525","author":"H Fassbender","year":"2017","unstructured":"Fassbender, H., Saltenberger, P.: On vector spaces of linearizations for matrix polynomials in orthogonal bases. Linear Algebra Appl. 525, 59\u201383 (2017)","journal-title":"Linear Algebra Appl."},{"key":"273_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2017.03.019","author":"H Fassbender","year":"2017","unstructured":"Fassbender, H., Saltenberger, P.: Block Kronecker ansatz spaces for matrix polynomials. Linear Algebra Appl. (2017). \n                    https:\/\/doi.org\/10.1016\/j.laa.2017.03.019","journal-title":"Linear Algebra Appl."},{"key":"273_CR18","doi-asserted-by":"publisher","first-page":"325","DOI":"10.1016\/S0024-3795(03)00548-2","volume":"372","author":"M Fiedler","year":"2003","unstructured":"Fiedler, M.: A note on companion matrices. Linear Algebra Appl. 372, 325\u2013331 (2003)","journal-title":"Linear Algebra Appl."},{"key":"273_CR19","volume-title":"Indefinite Linear Algebra and Applications","author":"I Gohberg","year":"2005","unstructured":"Gohberg, I., Lancaster, P., Rodman, L.: Indefinite Linear Algebra and Applications. Springer, Basel (2005)"},{"key":"273_CR20","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719024","volume-title":"Matrix Polynomials","author":"I Gohberg","year":"2009","unstructured":"Gohberg, I., Lancaster, P., Rodman, L.: Matrix Polynomials. SIAM, Philadelphia (2009)"},{"key":"273_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0962492917000034","volume":"26","author":"S G\u00fcttel","year":"2017","unstructured":"G\u00fcttel, S., Tisseur, F.: The nonlinear eigenvalue problem. Acta Numer. 26, 1\u201394 (2017)","journal-title":"Acta Numer."},{"issue":"3","key":"273_CR22","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2450153.2450156","volume":"39","author":"Sven Hammarling","year":"2013","unstructured":"Hammarling, S., Munro, C.J., Tisseur, F.: An algorithm for the complete solution of quadratic eigenvalue problems. ACM Trans. Math. Softw. 39, 18:1\u201318:19 (2013)","journal-title":"ACM Transactions on Mathematical Software"},{"key":"273_CR23","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1137\/060663738","volume":"29","author":"NJ Higham","year":"2007","unstructured":"Higham, N.J., Li, R.-C., Tisseur, F.: Backward error of polynomial eigenproblems solved by linearization. SIAM J. Matrix Anal. Appl. 29, 1218\u20131241 (2007)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR24","doi-asserted-by":"publisher","first-page":"1005","DOI":"10.1137\/050628283","volume":"28","author":"NJ Higham","year":"2006","unstructured":"Higham, N.J., Mackey, D.S., Tisseur, F.: The conditioning of linearizations of matrix polynomials. SIAM J. Matrix Anal. Appl. 28, 1005\u20131028 (2006)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR25","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1137\/050646202","volume":"29","author":"NJ Higham","year":"2006","unstructured":"Higham, N.J., Mackey, D.S., Mackey, N., Tisseur, F.: Symmetric linearizations for matrix polynomials. SIAM J. Matrix Anal. Appl. 29, 143\u2013159 (2006)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR26","doi-asserted-by":"publisher","first-page":"569","DOI":"10.1002\/nla.1913","volume":"21","author":"D Kressner","year":"2014","unstructured":"Kressner, D., Roman, J.: Memory-efficient Arnoldi algorithms for linearizations of matrix polynomials in Chebyshev basis. Numer. Linear Algebra Appl. 21, 569\u2013588 (2014)","journal-title":"Numer. Linear Algebra Appl."},{"key":"273_CR27","first-page":"146","volume":"8","author":"P Lancaster","year":"1961","unstructured":"Lancaster, P.: Symmetric transformations of the companion matrix. NABLA Bull. Malay. Math. Soc. 8, 146\u2013148 (1961)","journal-title":"NABLA Bull. Malay. Math. Soc."},{"key":"273_CR28","doi-asserted-by":"publisher","first-page":"123","DOI":"10.1137\/15M1015777","volume":"37","author":"P Lawrence","year":"2016","unstructured":"Lawrence, P., Van Barel, M., Van Dooren, P.: Backward error analysis of polynomial eigenvalue problems solved by linearization. SIAM J. Matrix Anal. Appl. 37, 123\u2013144 (2016)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR29","doi-asserted-by":"publisher","first-page":"192","DOI":"10.1137\/151005142","volume":"37","author":"D Lu","year":"2016","unstructured":"Lu, D., Su, Y., Bai, Z.: Stability analysis of the two-level orthogonal Arnoldi procedure. SIAM J. Matrix Anal. Appl. 37, 192\u2013214 (2016)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR30","first-page":"867","volume":"28","author":"DS Mackey","year":"2006","unstructured":"Mackey, D.S., Mackey, N., Mehl, C., Mehrmann, V.: Vector spaces of linearizations for matrix polynomials. SIAM J. Matrix Anal. Appl. 28, 867\u2013891 (2006)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR31","doi-asserted-by":"publisher","first-page":"1029","DOI":"10.1137\/050628362","volume":"28","author":"DS Mackey","year":"2006","unstructured":"Mackey, D.S., Mackey, N., Mehl, C., Mehrmann, V.: Structured polynomial eigenvalue problems: good vibrations from good linearizations. SIAM J. Matrix Anal. Appl. 28, 1029\u20131051 (2006)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR32","first-page":"971","volume":"432","author":"DS Mackey","year":"2010","unstructured":"Mackey, D.S., Mackey, N., Mehl, C., Mehrmann, V.: Jordan structures of alternating matrix polynomials. Linear Algebra Appl. 432, 971\u20131004 (2010)","journal-title":"Linear Algebra Appl."},{"key":"273_CR33","doi-asserted-by":"publisher","first-page":"53","DOI":"10.13001\/1081-3810.1426","volume":"22","author":"DS Mackey","year":"2011","unstructured":"Mackey, D.S., Mackey, N., Mehl, C., Mehrmann, V.: Smith forms of palindromic matrix polynomials. Electron. J. Linear Algebra 22, 53\u201391 (2011)","journal-title":"Electron. J. Linear Algebra"},{"key":"273_CR34","doi-asserted-by":"publisher","first-page":"4625","DOI":"10.1016\/j.laa.2013.02.010","volume":"438","author":"DS Mackey","year":"2013","unstructured":"Mackey, D.S., Mackey, N., Mehl, C., Mehrmann, V.: Skew-symmetric matrix polynomials and their Smith forms. Linear Algebra Appl. 438, 4625\u20134653 (2013)","journal-title":"Linear Algebra Appl."},{"key":"273_CR35","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1002\/gamm.201490007","volume":"27","author":"V Mehrmann","year":"2004","unstructured":"Mehrmann, V., Voss, H.: Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods. GAMM Mitt. Ges. Anqew. Math. Mech. 27, 121\u2013152 (2004)","journal-title":"GAMM Mitt. Ges. Anqew. Math. Mech."},{"key":"273_CR36","doi-asserted-by":"publisher","first-page":"241","DOI":"10.1137\/0710024","volume":"10","author":"CB Moler","year":"1973","unstructured":"Moler, C.B., Stewart, G.W.: An algorithm for generalized matrix eigenvalue problems. SIAM J. Numer. Anal. 10, 241\u2013256 (1973)","journal-title":"SIAM J. Numer. Anal."},{"key":"273_CR37","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/15M1013286","volume":"38","author":"Y Nakatsukasa","year":"2017","unstructured":"Nakatsukasa, Y., Noferini, V., Townsend, A.: Vector spaces of linearizations for matrix polynomials: a bivariate polynomial approach. SIAM J. Matrix Anal. Appl. 38, 1\u201329 (2017)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR38","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1016\/S0024-3795(99)00063-4","volume":"309","author":"F Tisseur","year":"2000","unstructured":"Tisseur, F.: Backward error and condition of polynomial eigenvalue problems. Linear Algebra Appl. 309, 339\u2013361 (2000)","journal-title":"Linear Algebra Appl."},{"key":"273_CR39","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1137\/S0895479802414783","volume":"26","author":"F Tisseur","year":"2004","unstructured":"Tisseur, F.: Tridiagonal-diagonal reduction of symmetric indefinite pairs. SIAM J. Matrix Anal. Appl. 26, 215\u2013232 (2004)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR40","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1137\/S0036144500381988","volume":"43","author":"F Tisseur","year":"2001","unstructured":"Tisseur, F., Meerbergen, K.: The quadratic eigenvalue problem. SIAM Rev. 43, 235\u2013286 (2001)","journal-title":"SIAM Rev."},{"key":"273_CR41","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2017.04.025","author":"M Van Barel","year":"2017","unstructured":"Van Barel, M., Tisseur, F.: Polynomial eigenvalue solver based on tropically scaled Lagrange linearization. Linear Algebra Appl. (2017). \n                    https:\/\/doi.org\/10.1016\/j.laa.2017.04.025","journal-title":"Linear Algebra Appl."},{"key":"273_CR42","doi-asserted-by":"publisher","first-page":"820","DOI":"10.1137\/140976698","volume":"36","author":"R Van Beeumen","year":"2015","unstructured":"Van Beeumen, R., Meerbergen, K., Michiels, W.: Compact rational Krylov methods for nonlinear eigenvalue problems. SIAM J. Matrix Anal. Appl. 36, 820\u2013838 (2015)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"273_CR43","doi-asserted-by":"publisher","first-page":"545","DOI":"10.1016\/0024-3795(83)90069-1","volume":"50","author":"P Van Dooren","year":"1983","unstructured":"Van Dooren, P., Dewilde, P.: The eigenstructure of an arbitrary polynomial matrix: computational aspects. Linear Algebra Appl. 50, 545\u2013579 (1983)","journal-title":"Linear Algebra Appl."},{"key":"273_CR44","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1137\/130921234","volume":"35","author":"L Zeng","year":"2014","unstructured":"Zeng, L., Su, Y.: A backward stable algorithm for quadratic eigenvalue problems. SIAM J. Matrix Anal. Appl. 35, 499\u2013516 (2014)","journal-title":"SIAM J. Matrix Anal. Appl."}],"container-title":["Calcolo"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10092-018-0273-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10092-018-0273-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10092-018-0273-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,16]],"date-time":"2020-05-16T18:53:11Z","timestamp":1589655191000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10092-018-0273-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,7,25]]},"references-count":44,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018,9]]}},"alternative-id":["273"],"URL":"https:\/\/doi.org\/10.1007\/s10092-018-0273-4","relation":{},"ISSN":["0008-0624","1126-5434"],"issn-type":[{"type":"print","value":"0008-0624"},{"type":"electronic","value":"1126-5434"}],"subject":[],"published":{"date-parts":[[2018,7,25]]},"assertion":[{"value":"16 January 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 July 2018","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 July 2018","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"32"}}