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As a consequence, all the eigenvectors computed by the algorithm come out numerically orthogonal to each other without making use of any reorthogonalization process. The key is first running a qd-type algorithm on the factored matrix LDL\n                    <jats:sup>t<\/jats:sup>\n                    and then applying a fine-tuned version of inverse iteration especially adapted to this situation. Since the computational cost is O(n) per eigenvector for an n \u00d7 n matrix, the proposed algorithm is the central step of a more ambitious algorithm which, at best (i.e., when all eigenvectors are well-conditioned), would compute all eigenvectors of an n \u00d7 n symmetric tridiagonal at O(n\n                    <jats:sup>2<\/jats:sup>\n                    ) cost, a great improvement over existing algorithms.\n                  <\/jats:p>","DOI":"10.1137\/s0895479800370111","type":"journal-article","created":{"date-parts":[[2004,4,1]],"date-time":"2004-04-01T21:00:51Z","timestamp":1080853251000},"page":"858-899","source":"Crossref","is-referenced-by-count":76,"title":["Orthogonal Eigenvectors and Relative Gaps"],"prefix":"10.1137","volume":"25","author":[{"given":"Inderjit S.","family":"Dhillon","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Beresford N.","family":"Parlett","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","unstructured":"ANSI\/IEEE,\n                      IEEE Standard for Binary Floating Point Arithmetic\n                      , Std 754\u20101985 ed., New York, 1985."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(00)00059-8"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(93)90202-Y"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(87)90102-9"},{"key":"R5","doi-asserted-by":"crossref","unstructured":"B. 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Parlett,\n                      Multiple representations to compute orthogonal eigenvectors of symmetric tridiagonal matrices\n                      , Linear Algebra Appl., to appear."},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/0732088"},{"key":"R12","unstructured":"S. C. Eisenstat and I. C. F. Ipsen,\n                      Relative perturbation bounds for eigenspaces and singular vector subspaces\n                      , in Proceedings of the Fifth SIAM Conference on Applied Linear Algebra, J. G. Lewis, ed., SIAM, 1994, pp. 62\u201366."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050024"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895294484"},{"key":"R15","doi-asserted-by":"crossref","unstructured":"J. G. F. Francis,\n                      The QR transformation, part I\n                      , Comput. 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