{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:31:04Z","timestamp":1787232664846,"version":"build-2736575974"},"reference-count":14,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM Rev."],"published-print":{"date-parts":[[2025,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>For many of the classic problems of linear algebra, effective and efficient numerical algorithms exist, particularly for situations where dimensions are not too large. The linear least squares problem is one such example: excellent algorithms exist when [Formula: see text] factorization is feasible. However, for large-dimensional (often sparse) linear least squares problems there\u00a0currently exist good solution algorithms only for well-conditioned problems or for problems where there are\u00a0lots of data but only a few variables in the solution. Such approaches ubiquitously employ normal equations and so have to contend with conditioning issues. We explore some alternative approaches that we characterize as not-normal equations where conditioning may not be such an issue.<\/jats:p>","DOI":"10.1137\/23m161851x","type":"journal-article","created":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T08:28:09Z","timestamp":1762417689000},"page":"865-872","source":"Crossref","is-referenced-by-count":0,"title":["Least Squares and the Not-Normal Equations"],"prefix":"10.1137","volume":"67","author":[{"given":"Andrew J.","family":"Wathen","sequence":"first","affiliation":[{"name":"Mathematical Institute, University of Oxford, Oxford, OX2 6GG, UK, and Computational Mathematics Group, Rutherford Appleton Laboratory, Didcot, OX11 0QX, UK."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,11,6]]},"reference":[{"key":"ref1","doi-asserted-by":"crossref","unstructured":"A. Bj\u00f6rck, Numerical Methods for Least Squares Problems, SIAM, Philadelphia, 1996.","DOI":"10.1137\/1.9781611971484"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(80)90158-5"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/10079687X"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1137\/090771806"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/BF03167519"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1137\/070696313"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1145\/355984.355989"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1093\/comjnl\/13.3.309"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.0804869105"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898718003"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1137\/0907058"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719574"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1017\/S0962492915000021"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/20M1387948"}],"container-title":["SIAM Review"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/23M161851X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,20]],"date-time":"2026-08-20T13:12:53Z","timestamp":1787231573000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/23M161851X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,6]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,12,31]]}},"alternative-id":["10.1137\/23M161851X"],"URL":"https:\/\/doi.org\/10.1137\/23m161851x","relation":{},"ISSN":["0036-1445","1095-7200"],"issn-type":[{"value":"0036-1445","type":"print"},{"value":"1095-7200","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,6]]}}}