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When the matrix equation pair <jats:italic>A<\/jats:italic><jats:italic>X<\/jats:italic><jats:italic>B<\/jats:italic> = <jats:italic>E<\/jats:italic>, <jats:italic>C<\/jats:italic><jats:italic>X<\/jats:italic><jats:italic>D<\/jats:italic> = <jats:italic>F<\/jats:italic> is consistent over generalized reflexive matrix <jats:italic>X<\/jats:italic>, for any generalized reflexive initial iterative matrix <jats:italic>X<\/jats:italic><jats:sub>1<\/jats:sub>, the generalized reflexive solution can be obtained by the iterative algorithm within finite iterative steps in the absence of round\u2010off errors. The unique least\u2010norm generalized reflexive iterative solution of the matrix equation pair can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate solution of <jats:italic>A<\/jats:italic><jats:italic>X<\/jats:italic><jats:italic>B<\/jats:italic> = <jats:italic>E<\/jats:italic>, <jats:italic>C<\/jats:italic><jats:italic>X<\/jats:italic><jats:italic>D<\/jats:italic> = <jats:italic>F<\/jats:italic> for a given generalized reflexive matrix <jats:italic>X<\/jats:italic><jats:sub>0<\/jats:sub> can be derived by finding the least\u2010norm generalized reflexive solution of a new corresponding matrix equation pair  with . Finally, several numerical examples are given to illustrate that our iterative algorithm is effective.<\/jats:p>","DOI":"10.1155\/2012\/492951","type":"journal-article","created":{"date-parts":[[2012,7,15]],"date-time":"2012-07-15T21:03:48Z","timestamp":1342386228000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["An Iterative Algorithm for the Generalized Reflexive Solution of the Matrix Equations <i>AXB<\/i> = <i>E<\/i>, <i>CXD<\/i> = <i>F<\/i>"],"prefix":"10.1155","volume":"2012","author":[{"given":"Deqin","family":"Chen","sequence":"first","affiliation":[]},{"given":"Feng","family":"Yin","sequence":"additional","affiliation":[]},{"given":"Guang-Xin","family":"Huang","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,7,15]]},"reference":[{"key":"e_1_2_6_1_2","doi-asserted-by":"publisher","DOI":"10.1137\/S0895479895288759"},{"volume-title":"Special Matrices","year":"2001","author":"Chen J. 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