{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T14:49:48Z","timestamp":1761662988250,"version":"3.41.2"},"reference-count":15,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2011,9,15]],"date-time":"2011-09-15T00:00:00Z","timestamp":1316044800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>This paper analyzes linear least squares problems with absolute quadratic constraints. We develop a generalized theory following Bookstein\u2032s conic\u2010fitting and Fitzgibbon\u2032s direct ellipse\u2010specific fitting. Under simple preconditions, it can be shown that a minimum always exists and can be determined by a generalized eigenvalue problem. This problem is numerically reduced to an eigenvalue problem by multiplications of Givens\u2032 rotations. Finally, four applications of this approach are presented.<\/jats:p>","DOI":"10.1155\/2012\/312985","type":"journal-article","created":{"date-parts":[[2011,9,16]],"date-time":"2011-09-16T02:02:37Z","timestamp":1316138557000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Least Squares Problems with Absolute Quadratic Constraints"],"prefix":"10.1155","volume":"2012","author":[{"given":"R.","family":"Sch\u00f6ne","sequence":"first","affiliation":[]},{"given":"T.","family":"Hanning","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2011,9,15]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2010.01.007"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1109\/TSMCB.2009.2028871"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2009.02.037"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.12.034"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.dsp.2009.10.012"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/0146-664X(79)90082-0"},{"key":"e_1_2_7_7_2","unstructured":"FitzgibbonA. 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