{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:09Z","timestamp":1787336949593,"version":"build-2736575974"},"reference-count":24,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[1999,1]]},"abstract":"<jats:p>One-sided orthogonal transformations which orthogonalize columns of a matrix are related to methods for finding singular values. They have the advantages of lending themselves to parallel and vector implementations and simplifying access to the data by not requiring access to both rows and columns. They can be used to find eigenvalues when the matrix is given in factored form. Here, a finite sequence of transformations leading to a partial orthogonalization of the columns is described. This permits a tridiagonal matrix whose eigenvalues are the squared singular values to be derived. The implementation on the Fujitsu VPP series is discussed and some timing results are presented.<\/jats:p>","DOI":"10.1137\/s1064827595296719","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"987-1005","source":"Crossref","is-referenced-by-count":1,"title":["A Parallel Algorithm for the Reduction to Tridiagonal Form for Eigendecomposition"],"prefix":"10.1137","volume":"21","author":[{"given":"Markus","family":"Hegland","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Margaret","family":"Kahn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Michael","family":"Osborne","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","unstructured":"E. Anderson, Z. Bai, C. Bischof, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, S. Ostrouchov, and D. Sorenson,\n                      Lapack Users\u2019 Guide\n                      , SIAM, Philadelphia, 1992."},{"key":"R2","unstructured":"Michael Berry, Ahmed Sameh, Multiprocessor Jacobi algorithms for dense symmetric eigenvalue and singular value decompositions, IEEE Comput. Soc. Press, Washington, DC, 1986, 433\u2013440954656"},{"key":"R3","doi-asserted-by":"crossref","unstructured":"Niloufer Mackey, A quaternion\u2010Jacobi method for symmetric matrices, Proc. Sympos. Appl. Math., Vol. 48, Amer. Math. 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Van Loan,\n                      Matrix Computations\n                      ,\n                      2nd ed\n                      ., The Johns Hopkins University Press, Baltimore, MD., 1989."},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1007\/BF02163027"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/0106005"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/15.3.271"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(87)90121-2"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/18.1.74"},{"key":"R17","unstructured":"B. N. Parlett,\n                      The Symmetric Eigenvalue Problem\n                      , Prentice\u2013Hall, New York, 1980."},{"key":"R18","doi-asserted-by":"crossref","unstructured":"R. M. S. Ralha,\n                      Parallel one\u2010sided Householder transformations for eigenvalues computation\n                      , in Proc. 1st Euromicro PDP Conf., IEEE Computer Society Press, Piscataway, NJ, 1993, pp. 218\u2013221.","DOI":"10.1109\/EMPDP.1993.336400"},{"key":"R19","unstructured":"C. Smith, B. Hendrickson, and E. Jessup,\n                      A parallel algorithm for Householder tridiagonalization\n                      , in Proc. Fifth SIAM Conf. Appl. Linear Alg., John G. Lewis, ed., SIAM, Philadelphia 1994, pp. 361\u2013365."},{"key":"R20","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4580-3"},{"key":"R21","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479894276369"},{"key":"R22","unstructured":"J. H. Wilkinson,\n                      The Algebraic Eigenvalue Problem\n                      , Oxford University Press, Oxford, 1965."},{"key":"R23","unstructured":"J. Wilkinson, A priori error analysis of algebraic processes, Izdat. \u201cMir\u201d, Moscow, 1968, 629\u201364038:1853"},{"key":"R24","doi-asserted-by":"publisher","DOI":"10.1006\/jpdc.1997.1304"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827595296719","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:37:48Z","timestamp":1787333868000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827595296719"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,1]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1999,1]]}},"alternative-id":["10.1137\/S1064827595296719"],"URL":"https:\/\/doi.org\/10.1137\/s1064827595296719","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,1]]}}}