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Intermediate quantities in the transformation furnish several attractive approximations to the smallest singular value.<\/jats:p><jats:p>The paper extols the advantages of using shifts with the algorithm. The nonorthogonal transformations improve accuracy.<\/jats:p>","DOI":"10.1002\/nla.1680020604","type":"journal-article","created":{"date-parts":[[2005,11,1]],"date-time":"2005-11-01T19:46:35Z","timestamp":1130874395000},"page":"507-531","source":"Crossref","is-referenced-by-count":6,"title":["Implicit Cholesky algorithms for singular values and vectors of triangular matrices"],"prefix":"10.1002","volume":"2","author":[{"given":"K.","family":"Vince Fernando","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Beresford N.","family":"Parlett","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2005,7,8]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"L. P.Ammann.Robust singular value decompositions: a new approach to projection pursuit. 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N.Faddeeva.Sur les syst\u00e8mes lin\u00e8aires alg\u00e8braiques de matrices rectangulaires et mal\u2010conditionn\u00e8es. Colloq. Int. du C.N.R.S. Besan\u00e7on 1966 No. 165 161\u2013170 1968."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01395779"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050024"},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","first-page":"787","DOI":"10.1090\/S0025-5718-1969-0258258-9","article-title":"Extensions and applications of the Householder algorithm for solving least squares problems","volume":"23","author":"Hanson R.","year":"1969","journal-title":"Math. Comp."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1137\/0106005"},{"key":"e_1_2_1_13_2","unstructured":"C. G. J.Jacobi.On a new way of solving the linear equations that arise in the method of least squares(Translated by G. W. Stewart). 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