{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T19:10:13Z","timestamp":1736190613535,"version":"3.32.0"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2005,12,23]],"date-time":"2005-12-23T00:00:00Z","timestamp":1135296000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2005,12,23]],"date-time":"2005-12-23T00:00:00Z","timestamp":1135296000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2006,2]]},"DOI":"10.1007\/s00211-005-0665-7","type":"journal-article","created":{"date-parts":[[2005,12,22]],"date-time":"2005-12-22T12:37:44Z","timestamp":1135255064000},"page":"709-726","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Orthogonal similarity transformation of a symmetric matrix into a diagonal-plus-semiseparable one with free choice of the diagonal"],"prefix":"10.1007","volume":"102","author":[{"given":"Raf","family":"Vandebril","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ellen Van","family":"Camp","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marc Van","family":"Barel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicola","family":"Mastronardi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2005,12,23]]},"reference":[{"key":"665_CR1","unstructured":"Bini, D.A., Gemignani, L., Pan, V.Y.: QR-like algorithms for generalized semiseparable matrices. Technical Report 1470, Department of Mathematics, University of Pisa, 2004"},{"key":"665_CR2","doi-asserted-by":"publisher","first-page":"723","DOI":"10.1007\/s00211-002-0199-1","volume":"96","author":"Chandrasekaran","year":"4","unstructured":"Chandrasekaran, S., Gu, M.: A divide and conquer algorithm for the eigendecomposition of symmetric block-diagonal plus semi-separable matrices. Numerische Mathematik 96(4), 723\u2013731 (2004)","journal-title":"Numerische Mathematik"},{"key":"665_CR3","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF01396757","volume":"36","author":"Cuppen","year":"1981","unstructured":"Cuppen, J.J.M.: A divide and conquer method for the symmetric tridiagonal eigenproblem. Numerische Mathematik 36, 177\u2013195 (1981)","journal-title":"Numerische Mathematik"},{"key":"665_CR4","doi-asserted-by":"crossref","unstructured":"Dewilde, P., van der Veen, A.-J.: Time-varying systems and computations. Kluwer academic publishers, Boston, June 1998","DOI":"10.1007\/978-1-4757-2817-0"},{"key":"665_CR5","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1016\/S0898-1221(97)00008-4","volume":"33","author":"Eidelman","year":"4","unstructured":"Eidelman, Y., Gohberg, I.C.: Inversion formulas and linear complexity algorithm for diagonal plus semiseparable matrices. Comput. Math. Appl. 33(4), 69\u201379 (1996)","journal-title":"Comput. Math. Appl."},{"key":"665_CR6","doi-asserted-by":"publisher","first-page":"743","DOI":"10.1002\/nla.448","volume":"12","author":"Fasino","year":"8","unstructured":"Fasino, D.: Rational Krylov matrices and QR-steps on Hermitian diagonal-plus- semiseparable matrices. To appear in Numerical Linear Algebra with Applications 12(8), 743\u2013754 (2005)","journal-title":"To appear in Numerical Linear Algebra with Applications"},{"key":"665_CR7","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1023\/B:NUMA.0000005402.66868.af","volume":"34","author":"Fasino","year":"2003","unstructured":"Fasino, D., Gemignani, L.: Direct and inverse eigenvalue problems, for diagonal-plus- semiseparable matrices. Numer. Algorithms 34, 313\u2013324 (2003)","journal-title":"Numer. Algorithms"},{"key":"665_CR8","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1090\/conm\/323\/05699","volume":"323","author":"Fasino","year":"2003","unstructured":"Fasino, D., Mastronardi, N., Van Barel, M.: Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form. Contemporary Math. 323, 105\u2013118 (2003)","journal-title":"Contemporary Math."},{"key":"665_CR9","doi-asserted-by":"crossref","unstructured":"Gantmacher, F.R., Krein, M.G.: Oscillation matrices and kernels and small vibrations of mechanical systems. AMS Chelsea Publishing, Providence, Rhode Island, revised edition, 2002","DOI":"10.1090\/chel\/345"},{"key":"665_CR10","unstructured":"Golub, G.H., Van Loan, C.F.: Matrix Computations. The Johns Hopkins University Press, third edition, 1996"},{"key":"665_CR11","unstructured":"Graybill, F.A.: Matrices with applications in statistics. Wadsworth international group, Belmont, California, 1983"},{"key":"665_CR12","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1023\/A:1021973919347","volume":"41","author":"Mastronardi","year":"1","unstructured":"Mastronardi, N., Chandrasekaran, S., Van Huffel, S.: Fast and stable algorithms for reducing diagonal plus semiseparable matrices to tridiagonal and bidiagonal form. BIT 41(1), 149\u2013157 2003","journal-title":"BIT"},{"key":"665_CR13","doi-asserted-by":"publisher","first-page":"379","DOI":"10.1007\/s11075-004-6998-y","volume":"39","author":"Mastronardi","year":"4","unstructured":"Mastronardi, N., Van Barel, M., Van Camp, E.: Divide and conquer algorithms for computing the eigendecomposition of symmetric diagonal-plus-semiseparable matrices. Numer. Algorithms 39(4), 379\u2013398 (2005)","journal-title":"Numer. Algorithms"},{"key":"665_CR14","unstructured":"Mastronardi, N., Van Barel, M., Vandebril, R.: Computing the rank revealing factorization by the semiseparable reduction. Technical Report TW418, Katholieke Universiteit Leuven, Dept. Computer Science, Celestijnenlaan 200A, 3001 Heverlee (Leuven), Belgium, May 2005"},{"key":"665_CR15","doi-asserted-by":"publisher","first-page":"707","DOI":"10.1137\/0613045","volume":"13","author":"Meurant","year":"1992","unstructured":"Meurant, G.: A review of the inverse of symmetric tridiagonal and block tridiagonal matrices. SIAM J. Matrix Anal. Appl. 13, 707\u2013728 (1992)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"665_CR16","doi-asserted-by":"crossref","unstructured":"Parlett, B.N.: The symmetric eigenvalue problem, volume 20 of Classics in Applied Mathematics. SIAM, Philadelphia, 1998","DOI":"10.1137\/1.9781611971163"},{"key":"665_CR17","doi-asserted-by":"crossref","first-page":"348","DOI":"10.1111\/j.2517-6161.1960.tb00381.x","volume":"22","author":"Roy","year":"1960","unstructured":"Roy, S.N., Greenberg, B.G., Sarhan, A.E.: Evaluation of determinants, characteristic equations and their roots for a class of patterned matrices. J. Royal Stat. Soc. Series B. Methodological 22, 348\u2013359 (1960)","journal-title":"J. Royal Stat. Soc. Series B. Methodological"},{"key":"665_CR18","doi-asserted-by":"crossref","unstructured":"Van Barel, M., Fasino, D., Gemignani, L., Mastronardi, N.: Orthogonal rational functions and diagonal plus semiseparable matrices. In: Advanced Signal Processing Algorithms, Architectures, and Implementations XII, F. T. Luk, (ed.), volume 4791 of Proceedings of SPIE, 2002 pp 167\u2013170","DOI":"10.1117\/12.453815"},{"key":"665_CR19","doi-asserted-by":"publisher","first-page":"176","DOI":"10.1137\/S0895479803428229","volume":"27","author":"Barel","year":"1","unstructured":"Van Barel, M., Vandebril, R., Mastronardi, N.: An orthogonal similarity reduction of a matrix into semiseparable form. SIAM Journal on Matrix Analysis and its Applications, 27(1), 176\u2013197 (2005)","journal-title":"SIAM Journal on Matrix Analysis and its Applications,"},{"key":"665_CR20","doi-asserted-by":"crossref","first-page":"731","DOI":"10.1016\/j.cam.2003.09.040","volume":"164\u2013165","author":"E. Camp","year":"2004","unstructured":"Van Camp, E., Mastronardi, N., Van Barel, M.: Two fast algorithms for solving diagonal-plus-semiseparable linear systems. J. Comput. Appl. Math. 164\u2013165, 731\u2013747 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"665_CR21","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1002\/nla.425","volume":"12","author":"Vandebril","year":"7","unstructured":"Vandebril, R., Van Barel, M., Mastronardi, N.: An implicit QR-algorithm for symmetric semiseparable matrices. Numerical Linear Algebra with Applications 12(7), 625\u2013658 (2005)","journal-title":"Numerical Linear Algebra with Applications"},{"key":"665_CR22","doi-asserted-by":"publisher","first-page":"839","DOI":"10.1002\/nla.455","volume":"12","author":"Vandebril","year":"8","unstructured":"Vandebril, R., Van Barel, M., Mastronardi, N.: A note on the representation and definition of semiseparable matrices. Numerical Linear Algebra with Applications 12(8), 839\u2013858 (2005)","journal-title":"Numerical Linear Algebra with Applications"},{"key":"665_CR23","unstructured":"Vandebril, R., Van Camp, E., Van Barel, M., Mastronardi, N.: On the convergence properties of the orthogonal similarity transformations to tridiagonal and semiseparable (plus diagonal) form. Report TW436, Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200A, B-3001 Leuven (Heverlee), Belgium, Aug 2005."},{"key":"665_CR24","first-page":"687","volume":"70","author":"Watkins","year":"1991","unstructured":"Watkins, D.S.: On QR algorithms for the eigenvalue problem. Nato adv. sci. inst. ser. f comput systems sci. 70, 687\u2013693 (1991)","journal-title":"Nato adv. sci. inst. ser. f comput systems sci."},{"key":"665_CR25","unstructured":"Wilkinson, J.H.: The algebraic eigenvalue problem. Numerical mathematics and scientific computation. Oxford University Press, Great Claredon Street, Oxford OX2 6DP, 1999"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-005-0665-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00211-005-0665-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-005-0665-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-005-0665-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,1,6]],"date-time":"2025-01-06T18:31:31Z","timestamp":1736188291000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00211-005-0665-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,12,23]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,2]]}},"alternative-id":["665"],"URL":"https:\/\/doi.org\/10.1007\/s00211-005-0665-7","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"type":"print","value":"0029-599X"},{"type":"electronic","value":"0945-3245"}],"subject":[],"published":{"date-parts":[[2005,12,23]]},"assertion":[{"value":"4 August 2004","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 December 2005","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}