{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:40:13Z","timestamp":1787323213869,"version":"3.56.0"},"reference-count":7,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[1996,7]]},"abstract":"<jats:p>The aim of this note is to show that the matrix $S( n,\\alpha ) = ( 1 - \\alpha ) I + \\alpha ee^\\tau , \\, e = (1,\\cdots,1)^\\tau , \\,\\alpha \\in ( 0,1 )$ is not a counterexample for the accuracy properties of the Jacobi method for computing the singular and eigenvalue decomposition, as might be understood from a recent article of Mascarenhas in this journal. In fact, the Jacobi process on $S( n,\\alpha )$ is an example of the perfect behaviour of the algorithm. It is shown that Jacobi rotations preserve the optimal (with respect to diagonal scalings) spectral condition number of $S( n,\\alpha )$.<\/jats:p>","DOI":"10.1137\/s0895479894261711","type":"journal-article","created":{"date-parts":[[2005,2,27]],"date-time":"2005-02-27T07:15:07Z","timestamp":1109488507000},"page":"509-514","source":"Crossref","is-referenced-by-count":4,"title":["On the Condition Behaviour in the Jacobi Method"],"prefix":"10.1137","volume":"17","author":[{"given":"Zlatko","family":"Drama\u010d","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","unstructured":"J. Demmel,  Open Problems in Numerical Linear Algebra, LAPACK Working Note, 47, Computer Science Division and Mathematics Department, University of California, Berkeley, CA,  1992"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1137\/0613074"},{"key":"R3","unstructured":"Z. Drma\u010d, Ph.D. Thesis,  Computing the Singular and the Generalized Singular Values, Lehrgebiet Mathematische Physik, University of Hagen, D-58084 Hagen, Germany,  1994"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1955-0069585-4"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1515\/crll.1846.30.51"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S089547989222792X"},{"key":"R7","unstructured":"X. Wang,  A few propositions on upper bounds for  max0\u2264m\u2264Mk(Am)\/k(A0),  1991, University of Hagen, D-58084 Hagen, Germany, unpublished manuscript"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479894261711","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:48:04Z","timestamp":1787320084000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479894261711"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,7]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1996,7]]}},"alternative-id":["10.1137\/S0895479894261711"],"URL":"https:\/\/doi.org\/10.1137\/s0895479894261711","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,7]]}}}