{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T16:29:09Z","timestamp":1787329749735,"version":"build-2736575974"},"reference-count":15,"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":[[1998,1]]},"abstract":"<jats:p>The weighted generalized inverses have several important applications in researching the singular matrices, regularization methods for ill-posed problems, optimization problems, and statistics problems. In this paper we establish some sufficient and necessary conditions for inverse order rule of weighted generalized inverse.<\/jats:p>","DOI":"10.1137\/s0895479896305441","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"772-775","source":"Crossref","is-referenced-by-count":58,"title":["Inverse Order Rule for Weighted Generalized Inverse"],"prefix":"10.1137","volume":"19","author":[{"given":"Wenyu","family":"Sun","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yimin","family":"Wei","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,31]]},"reference":[{"key":"R1","first-page":"621","volume":"42","author":"Arghiriade Emmanuel","year":"1967","journal-title":"Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8)"},{"key":"R2","volume-title":"Generalized inverses: theory and applications","author":"Ben\u2010Israel Adi","year":"1980"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1080\/10556789608805637"},{"key":"R4","unstructured":"G. H. Golub and C. F. Van Loan,\n                      Matrix Computations\n                      , The Johns Hopkins University Press, Baltimore, MD, 1983."},{"key":"R5","volume-title":"Guangyi ni juzhen yinlun","author":"He Xu","year":"1991"},{"key":"R6","unstructured":"C. R. Rao and S. K. Mitra,\n                      Generalized Inverse of Matrices and Its Applications\n                      , John Wiley, New York, 1971."},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(96)00112-9"},{"key":"R8","first-page":"117","volume":"3","author":"Sun Wen","year":"1986","journal-title":"Nanjing Daxue Xuebao Shuxue Bannian Kan"},{"key":"R9","unstructured":"W. Sun, J. Yuan, and Y. Yuan,\n                      Trust region method of conic model for linearly constrained optimization\n                      , J. Optim. Theory Appl., submitted."},{"key":"R10","unstructured":"W. Sun and Y. Yuan,\n                      Trust Region Method of Conic Model for Nonlinearly Constrained Optimization\n                      , Math. Comp., submitted."},{"key":"R11","doi-asserted-by":"crossref","unstructured":"Hoang Tuy, D.C. optimization: theory, methods and algorithms, Nonconvex Optim. Appl., Vol. 2, Kluwer Acad. Publ., Dordrecht, 1995, 149\u201321698b:90108","DOI":"10.1007\/978-1-4615-2025-2_4"},{"key":"R12","first-page":"48","volume":"1","author":"Wang G.","year":"1987","journal-title":"Appl. Math. Comput. Math."},{"key":"R13","unstructured":"Hans Werner, g\u2010inverses of matrix products, Eul, Bergisch Gladbach, 1992, 531\u20135461248855"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(94)90474-X"},{"key":"R15","unstructured":"Z. Z. Yu and Z. L. Yu,\n                      Weighted generalized inverse and rank\u2010deficient variance of network\n                      , J. Wuhan Surveying and Drawing College, 1 (1985)."}],"container-title":["SIAM Journal on Matrix Analysis and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S0895479896305441","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:32:01Z","timestamp":1787326321000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S0895479896305441"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1137\/S0895479896305441"],"URL":"https:\/\/doi.org\/10.1137\/s0895479896305441","relation":{},"ISSN":["0895-4798","1095-7162"],"issn-type":[{"value":"0895-4798","type":"print"},{"value":"1095-7162","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}