{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:07:16Z","timestamp":1758823636325},"reference-count":9,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[2004,4,1]],"date-time":"2004-04-01T00:00:00Z","timestamp":1080777600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2004,4]]},"DOI":"10.1016\/s0096-3003(03)00360-6","type":"journal-article","created":{"date-parts":[[2003,5,19]],"date-time":"2003-05-19T16:51:58Z","timestamp":1053363118000},"page":"533-541","source":"Crossref","is-referenced-by-count":14,"title":["On positive definite solutions of the nonlinear matrix equation X+A\u2605X\u2212nA=I"],"prefix":"10.1016","volume":"151","author":[{"given":"Salah M.","family":"El-Sayed","sequence":"first","affiliation":[]},{"given":"Asmaa M.","family":"Al-Dbiban","sequence":"additional","affiliation":[]}],"member":"78","reference":[{"key":"10.1016\/S0096-3003(03)00360-6_BIB1","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0024-3795(90)90005-W","article-title":"Positive solution to X=A\u2212BX\u22121B\u2605","volume":"134","author":"Anderson","year":"1990","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/S0096-3003(03)00360-6_BIB2","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/0024-3795(93)90295-Y","article-title":"Necessary and sufficient conditions for the existence of a positive definite solution of the matrix equation X+A\u2605X\u22121A=Q","volume":"186","author":"Engwerda","year":"1993","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/S0096-3003(03)00360-6_BIB3","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/0024-3795(93)90115-5","article-title":"On the existence of a positive definite solution of the matrix equation X+ATX\u22121A=I","volume":"194","author":"Engwerda","year":"1993","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/S0096-3003(03)00360-6_BIB4","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/S0024-3795(98)00023-8","article-title":"Properties of positive definite solutions of the equation X+A\u2605X\u22122A=I","volume":"279","author":"Ivanov","year":"1998","journal-title":"Linear Algebra Appl."},{"key":"10.1016\/S0096-3003(03)00360-6_BIB5","doi-asserted-by":"crossref","first-page":"1589","DOI":"10.1090\/S0025-5718-99-01122-9","article-title":"Iterative solution of two matrix equations","volume":"68","author":"Guo","year":"1999","journal-title":"Math. Comput."},{"key":"10.1016\/S0096-3003(03)00360-6_BIB6","series-title":"Theory of Matrices","author":"Lancaster","year":"1969"},{"key":"10.1016\/S0096-3003(03)00360-6_BIB7","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1137\/S0895479899345571","article-title":"On the iteration method for solving a class of nonlinear matrix equations","volume":"23","author":"El-Sayed","year":"2001","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"10.1016\/S0096-3003(03)00360-6_BIB8","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1016\/S0096-3003(01)00019-4","article-title":"Some properties for the existence of a positive definite solution of matrix equation X+A\u2605X\u22122mA=I","volume":"128","author":"El-Sayed","year":"2002","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/S0096-3003(03)00360-6_BIB9","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1016\/0024-3795(95)00120-4","article-title":"On the matrix equation X+ATX\u22121A=I","volume":"247","author":"Zhan","year":"1996","journal-title":"Linear Algebra Appl."}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300303003606?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300303003606?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2019,3,21]],"date-time":"2019-03-21T11:55:01Z","timestamp":1553169301000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300303003606"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,4]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2004,4]]}},"alternative-id":["S0096300303003606"],"URL":"https:\/\/doi.org\/10.1016\/s0096-3003(03)00360-6","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2004,4]]}}}