{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T20:15:49Z","timestamp":1742933749373,"version":"3.40.3"},"publisher-location":"Berlin, Heidelberg","reference-count":20,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642019692"},{"type":"electronic","value":"9783642019708"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"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":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-01970-8_47","type":"book-chapter","created":{"date-parts":[[2009,5,19]],"date-time":"2009-05-19T18:26:23Z","timestamp":1242757583000},"page":"481-490","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Non-splitting Tridiagonalization of Complex Symmetric Matrices"],"prefix":"10.1007","author":[{"given":"W. N.","family":"Gansterer","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"A. R.","family":"Gruber","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Pacher","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"47_CR1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511810817","volume-title":"Matrix Analysis","author":"R.A. Horn","year":"1985","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1985)"},{"key":"47_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"945","DOI":"10.1007\/978-3-540-69384-0_99","volume-title":"Computational Science \u2013 ICCS 2008","author":"W.N. Gansterer","year":"2008","unstructured":"Gansterer, W.N., Schabauer, H., Pacher, C., Finger, N.: Tridiagonalizing complex symmetric matrices in waveguide simulations. In: Bubak, M., van Albada, G.D., Dongarra, J., Sloot, P.M.A. (eds.) ICCS 2008, Part I. LNCS, vol.\u00a05101, pp. 945\u2013954. Springer, Heidelberg (2008)"},{"issue":"1","key":"47_CR3","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1145\/225545.225551","volume":"22","author":"R.W. Freund","year":"1996","unstructured":"Freund, R.W., Nachtigal, N.M.: QMRPACK: a package of QMR algorithms. ACM Trans. Math. Softw.\u00a022(1), 46\u201377 (1996)","journal-title":"ACM Trans. Math. Softw."},{"key":"47_CR4","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/77626.79170","volume":"16","author":"J.J. Dongarra","year":"1990","unstructured":"Dongarra, J.J., Du Croz, J., Duff, I.S., Hammarling, S.: A set of level 3 basic linear algebra subprograms. ACM Trans. Math.\u00a016, 1\u201317, 18\u201328 (1990)","journal-title":"ACM Trans. Math."},{"key":"47_CR5","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719604","volume-title":"Lapack Users Guide","author":"E. Anderson","year":"1999","unstructured":"Anderson, E., Bai, Z., Bischof, C.H., Blackford, S., Demmel, J.W., Dongarra, J.J., Du Croz, J., Greenbaum, A., Hammarling, S., McKenney, A., Sorensen, D.C.: Lapack Users Guide, 3rd edn. SIAM Press, Philadelphia (1999)","edition":"3"},{"key":"47_CR6","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719642","volume-title":"ScaLapack Users\u2019 Guide","author":"L.S. Blackford","year":"1997","unstructured":"Blackford, L.S., Choi, J., Cleary, A., D\u2019Azevedo, E., Demmel, J.W., Dhillon, I., Dongarra, J.J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D., Whaley, R.C.: ScaLapack Users\u2019 Guide. SIAM Press, Philadelphia (1997)"},{"key":"47_CR7","volume-title":"Using PLapack: Parallel Linear Algebra Package","author":"R. van de Geijn","year":"1997","unstructured":"van de Geijn, R.: Using PLapack: Parallel Linear Algebra Package. The MIT Press, Cambridge (1997)"},{"issue":"1","key":"47_CR8","doi-asserted-by":"publisher","first-page":"137","DOI":"10.1137\/0914009","volume":"14","author":"R.W. Freund","year":"1993","unstructured":"Freund, R.W., Gutknecht, M.H., Nachtigal, N.M.: An implementation of the look-ahead Lanczos algorithm for non-hermitian matrices. SIAM J. Sci. Comput.\u00a014(1), 137\u2013158 (1993)","journal-title":"SIAM J. Sci. Comput."},{"key":"47_CR9","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1016\/S0304-0208(08)72647-1","volume-title":"Proceedings of the IBM Europe Institute Workshop on Large Scale Eigenvalue Problems","author":"J.K. Cullum","year":"1986","unstructured":"Cullum, J.K., Willoughby, R.A.: A practical procedure for computing eigenvalues of large sparse nonsymmetric matrices. In: Cullum, J.K., Willoughby, R.A. (eds.) Proceedings of the IBM Europe Institute Workshop on Large Scale Eigenvalue Problems, pp. 193\u2013223. North-Holland, Amsterdam (1986)"},{"issue":"4","key":"47_CR10","doi-asserted-by":"publisher","first-page":"627","DOI":"10.1006\/jsvi.1995.0337","volume":"184","author":"A.Y.T. Leung","year":"1995","unstructured":"Leung, A.Y.T.: Subspace iteration for complex symmetric eigenproblems. J. Sound Vibration\u00a0184(4), 627\u2013637 (1995)","journal-title":"J. Sound Vibration"},{"issue":"5","key":"47_CR11","doi-asserted-by":"publisher","first-page":"1655","DOI":"10.1137\/S1064827502410992","volume":"25","author":"P. Arbenz","year":"2004","unstructured":"Arbenz, P., Hochstenbach, M.E.: A Jacobi\u2013Davidson method for solving complex symmetric eigenvalue problems. SIAM J. Sci. Comput.\u00a025(5), 1655\u20131673 (2004)","journal-title":"SIAM J. Sci. Comput."},{"volume-title":"Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide","year":"2000","key":"47_CR12","unstructured":"Bai, Z., Demmel, J., Dongarra, J.J., Ruhe, A., van der Vorst, H. (eds.): Templates for the Solution of Algebraic Eigenvalue Problems: A Practical Guide. SIAM Press, Philadelphia (2000)"},{"key":"47_CR13","doi-asserted-by":"publisher","first-page":"4903","DOI":"10.1088\/0305-4470\/25\/18\/022","volume":"25","author":"K. Ohnami","year":"1992","unstructured":"Ohnami, K., Mikami, Y.: Resonance scattering in a two-dimensional non-integrable system. J. Phys. A\u00a025, 4903\u20134912 (1992)","journal-title":"J. Phys. A"},{"key":"47_CR14","doi-asserted-by":"publisher","first-page":"1412","DOI":"10.1137\/S1064827594269056","volume":"18","author":"I. Bar-On","year":"1997","unstructured":"Bar-On, I., Ryaboy, V.: Fast diagonalization of large and dense complex symmetric matrices, with applications to quantum reaction dynamics. SIAM J. Sci. Comput.\u00a018, 1412\u20131435 (1997)","journal-title":"SIAM J. Sci. Comput."},{"key":"47_CR15","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1137\/S0895479894137639","volume":"17","author":"J.K. Cullum","year":"1996","unstructured":"Cullum, J.K., Willoughby, R.A.: A QL procedure for computing the eigenvalues of complex symmetric tridiagonal matrices. SIAM J. Matrix Anal. Appl.\u00a017, 83\u2013109 (1996)","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"47_CR16","doi-asserted-by":"crossref","unstructured":"Luk, F., Qiao, S.: Using complex-orthogonal transformations to diagonalize a complex symmetric matrix. In: Luk, F.T. (ed.) Advanced Signal Processing: Algorithms, Architectures, and Implementations VII, Proc. SPIE, vol.\u00a0(3162), pp. 418\u2013425 (1997)","DOI":"10.1117\/12.284193"},{"key":"47_CR17","volume-title":"Lanczos Algorithms for Large Symmetric Eigenvalue Computations, vol. 1: Theory, vol. 2: Programs","author":"J.K. Cullum","year":"1985","unstructured":"Cullum, J.K., Willoughby, R.A.: Lanczos Algorithms for Large Symmetric Eigenvalue Computations, vol. 1: Theory, vol. 2: Programs. Birkh\u00e4user, Boston (1985)"},{"key":"47_CR18","doi-asserted-by":"publisher","first-page":"433","DOI":"10.2307\/2004005","volume":"17","author":"C.D. La Budde","year":"1963","unstructured":"La Budde, C.D.: The reduction of an arbitrary real square matrix to tridiagonal form using similarity transformations. Math. Comp.\u00a017, 433\u2013437 (1963)","journal-title":"Math. Comp."},{"key":"47_CR19","doi-asserted-by":"publisher","first-page":"501","DOI":"10.1090\/S0025-5718-1964-0165670-0","volume":"18","author":"H.H. Wang","year":"1964","unstructured":"Wang, H.H., Gregory, R.T.: On the reduction of an arbitrary real square matrix to tridiagonal form. Math. Comp.\u00a018, 501\u2013505 (1964)","journal-title":"Math. Comp."},{"key":"47_CR20","first-page":"505","volume":"18","author":"B.N. Parlett","year":"1964","unstructured":"Parlett, B.N.: A note on La Budde\u2019s algorithm. Math. Comp.\u00a018, 505\u2013506 (1964)","journal-title":"Math. Comp."}],"container-title":["Lecture Notes in Computer Science","Computational Science \u2013 ICCS 2009"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-01970-8_47","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,12,24]],"date-time":"2021-12-24T09:13:36Z","timestamp":1640337216000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-642-01970-8_47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642019692","9783642019708"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-01970-8_47","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2009]]},"assertion":[{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}