{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:29:11Z","timestamp":1787336951513,"version":"build-2736575974"},"reference-count":11,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Matrix Anal. Appl."],"published-print":{"date-parts":[[2003,1]]},"abstract":"<jats:p>In this paper we show how to compute recursively an approximation of the left and right dominant singular subspaces of a given matrix. In order to perform as few as possible operations on each column of the matrix, we use a variant of the classical Gram-Schmidt algorithm to estimate this subspace. The method is shown to be particularly suited for matrices with many more rows than columns. Bounds for the accuracy of the computed subspace are provided. Moreover, the analysis of error propagation in this algorithm provides new insights in the loss of orthogonality typically observed in the classical Gram-Schmidt method.<\/jats:p>","DOI":"10.1137\/s0895479803374657","type":"journal-article","created":{"date-parts":[[2003,9,19]],"date-time":"2003-09-19T21:40:15Z","timestamp":1064007615000},"page":"445-463","source":"Crossref","is-referenced-by-count":19,"title":["Recursive Calculation of Dominant Singular Subspaces"],"prefix":"10.1137","volume":"25","author":[{"given":"Y.","family":"Chahlaoui","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"K.","family":"Gallivan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Van Dooren","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01939404"},{"key":"R2","unstructured":"C. G. Baker,\n                      An Incremental Block Algorithm for Tracking Dominant Singular Subspaces\n                      , Technical Report FSU\u2010CSIT\u201003\u201003, CSIT, Florida State University, Tallahassee, FL, 2003."},{"key":"R3","unstructured":"Younes Chahlaoui, Kyle Gallivan, Paul Van Dooren, An incremental method for computing dominant singular spaces, SIAM, Philadelphia, PA, 2001, 53\u2013621861814"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1145\/355984.355990"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1006\/gmip.1997.0425"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479896297720"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176994775"},{"key":"R8","volume-title":"Matrix computations","author":"Golub Gene","year":"1983"},{"key":"R9","volume-title":"Accuracy and stability of numerical algorithms","author":"Higham Nicholas","year":"1996"},{"key":"R10","volume-title":"Matrix perturbation theory","author":"Stewart G.","year":"1990"},{"key":"R11","unstructured":"P. Van Dooren, Gramian based model reduction of large\u2010scale dynamical systems, Chapman & Hall\/CRC Res. Notes Math., Vol. 420, Chapman & Hall\/CRC, Boca Raton, FL, 2000, 231\u20132472001a:93034"}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479803374657","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:38:04Z","timestamp":1787333884000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479803374657"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,1]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2003,1]]}},"alternative-id":["10.1137\/S0895479803374657"],"URL":"https:\/\/doi.org\/10.1137\/s0895479803374657","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,1]]}}}