{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T12:17:51Z","timestamp":1712319471996},"reference-count":21,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2008,8,22]],"date-time":"2008-08-22T00:00:00Z","timestamp":1219363200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Linear Algebra App"],"published-print":{"date-parts":[[2009,1]]},"abstract":"Abstract<\/jats:title>We present structure\u2010preserving numerical methods for the eigenvalue problem of complex palindromic pencils. Such problems arise in control theory, as well as from palindromic linearizations of higher degree palindromic matrix polynomials. A key ingredient of these methods is the development of an appropriate condensed form\u2014the anti\u2010triangular Schur form. Ill\u2010conditioned problems with eigenvalues near the unit circle, in particular near \u00b11, are discussed. We show how a combination of unstructured methods followed by a structured refinement can be used to solve such problems accurately. Copyright \u00a9 2008 John Wiley & Sons, Ltd.<\/jats:p>","DOI":"10.1002\/nla.612","type":"journal-article","created":{"date-parts":[[2008,8,22]],"date-time":"2008-08-22T10:38:15Z","timestamp":1219401495000},"page":"63-86","source":"Crossref","is-referenced-by-count":35,"title":["Numerical methods for palindromic eigenvalue problems: Computing the anti\u2010triangular Schur form"],"prefix":"10.1002","volume":"16","author":[{"given":"D. Steven","family":"Mackey","sequence":"first","affiliation":[]},{"given":"Niloufer","family":"Mackey","sequence":"additional","affiliation":[]},{"given":"Christian","family":"Mehl","sequence":"additional","affiliation":[]},{"given":"Volker","family":"Mehrmann","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2008,8,22]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"ByersR KressnerD.Exploiting bistructured computational problems. Sixth International Workshop on Accurate Solution of Eigenvalue Problems Pennsylvania State University University Park May 2006."},{"key":"e_1_2_1_3_2","unstructured":"ByersR MackeyDS MehrmannV XuH. Symplectic BVD and palindromic approaches to discrete\u2010time control problems. Preprint 14\u20102008 Institut f\u00fcr Mathematik TU Berlin D\u201010623 Berlin FRG 2008. url:http:\/\/www.math.tu\u2010berlin.de\/preprints\/."},{"key":"e_1_2_1_4_2","article-title":"Vibration of fast trains, palindromic eigenvalue problems and structure\u2010preserving doubling algorithms","author":"Chu K\u2010WE","year":"2007","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1109\/TC.1987.1676879"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/2002135"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01386312"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1137\/050646202"},{"key":"e_1_2_1_9_2","unstructured":"HilligesA.Numerische L\u00f6sung von quadratischen Eigenwertproblemen mit Anwendung in der Schienendynamik. Diplomarbeit TU Berlin Institut f\u00fcr Mathematik 2004."},{"key":"e_1_2_1_10_2","unstructured":"HilligesA MehlC MehrmannV.On the solution of palindromic eigenvalue problems. Proceedings of the 4th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS) Jyv\u00e4skyl\u00e4 Finland 2004. CD\u2010ROM."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1109\/TUFFC.2006.1642518"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","unstructured":"KressnerD Schr\u00f6derC WatkinsDS.Implicit QR algorithms for palindromic and even eigenvalue problems. Preprint 432 TU Berlin MATHEON Germany January2008.","DOI":"10.1007\/s11075-008-9226-3"},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","volume-title":"The Algebraic Riccati Equation","author":"Lancaster P","year":"1995","DOI":"10.1093\/oso\/9780198537953.001.0001"},{"key":"e_1_2_1_14_2","volume-title":"The Theory of Matrices","author":"Lancaster P","year":"1985"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.1979.1102178"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1137\/050628362"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1137\/060663246"},{"key":"e_1_2_1_18_2","doi-asserted-by":"publisher","DOI":"10.1137\/S089547980240947X"},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0039443"},{"key":"e_1_2_1_20_2","first-page":"106","article-title":"Polynomial eigenvalue problems with Hamiltonian structure","volume":"13","author":"Mehrmann V","year":"2002","journal-title":"Electronic Transactions on Numerical Analysis"},{"key":"e_1_2_1_21_2","unstructured":"Schr\u00f6derC.URV decomposition based structured methods for palindromic and even eigenvalue problems. Preprint 375 TU Berlin Matheon Germany March2007; submitted."},{"key":"e_1_2_1_22_2","unstructured":"ZaglmayrS.Eigenvalue problems in SAW\u2010filter simulations. Diplomarbeit Institute of Computational Mathematics J. Kepler University Linz Austria 2002."}],"container-title":["Numerical Linear Algebra with Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fnla.612","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/nla.612","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T19:13:43Z","timestamp":1699902823000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/nla.612"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8,22]]},"references-count":21,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,1]]}},"alternative-id":["10.1002\/nla.612"],"URL":"https:\/\/doi.org\/10.1002\/nla.612","archive":["Portico"],"relation":{},"ISSN":["1070-5325","1099-1506"],"issn-type":[{"value":"1070-5325","type":"print"},{"value":"1099-1506","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,8,22]]}}}