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When the matrix equations are consistent, for any initial generalized reflexive matrix pair [<jats:italic>X<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>Y<\/jats:italic><jats:sub>1<\/jats:sub>], the generalized reflexive solutions can be obtained by the iterative algorithm within finite iterative steps in the absence of round\u2010off errors, and the least Frobenius norm generalized reflexive solutions can be obtained by choosing a special kind of initial matrix pair. The unique optimal approximation generalized reflexive solution pair  to a given matrix pair [<jats:italic>X<\/jats:italic><jats:sub>0<\/jats:sub>, <jats:italic>Y<\/jats:italic><jats:sub>0<\/jats:sub>] in Frobenius norm can be derived by finding the least\u2010norm generalized reflexive solution pair  of a new corresponding generalized coupled Sylvester matrix equation pair , where . Several numerical examples are given to show the effectiveness of the presented iterative algorithm.<\/jats:p>","DOI":"10.1155\/2012\/152805","type":"journal-article","created":{"date-parts":[[2012,8,26]],"date-time":"2012-08-26T21:00:50Z","timestamp":1346014850000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An Iterative Algorithm for the Generalized Reflexive Solutions of the Generalized Coupled Sylvester Matrix Equations"],"prefix":"10.1155","volume":"2012","author":[{"given":"Feng","family":"Yin","sequence":"first","affiliation":[]},{"given":"Guang-Xin","family":"Huang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,8,26]]},"reference":[{"key":"e_1_2_8_1_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895288759"},{"volume-title":"Special Matrices","year":"2001","author":"Chen J. 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