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When the matrix equation is consistent over reflexive matrix<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>X<\/mml:mi><\/mml:mrow><\/mml:math>, a reflexive solution can be obtained within finite iteration steps in the absence of roundoff errors. By the proposed iterative algorithm, the least Frobenius norm reflexive solution of the matrix equation can be derived when an appropriate initial iterative matrix is chosen. Furthermore, the optimal approximate reflexive solution to a given reflexive matrix<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:msub><mml:mi>X<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><\/mml:mrow><\/mml:math>can be derived by finding the least Frobenius norm reflexive solution of a new corresponding quaternion matrix equation. Finally, two numerical examples are given to illustrate the efficiency of the proposed methods.<\/jats:p>","DOI":"10.1155\/2013\/217540","type":"journal-article","created":{"date-parts":[[2013,2,24]],"date-time":"2013-02-24T21:01:40Z","timestamp":1361739700000},"page":"1-14","source":"Crossref","is-referenced-by-count":2,"title":["An Efficient Algorithm for the Reflexive Solution of the Quaternion Matrix Equation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>A<\/mml:mi><mml:mi>X<\/mml:mi><mml:mi>B<\/mml:mi><mml:mo>+<\/mml:mo><mml:mi>C<\/mml:mi><mml:msup><mml:mi>X<\/mml:mi><mml:mi>H<\/mml:mi><\/mml:msup><mml:mi>D<\/mml:mi><mml:mo>=<\/mml:mo><mml:mi>F<\/mml:mi><\/mml:mrow><\/mml:math>"],"prefix":"10.1155","volume":"2013","author":[{"given":"Ning","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematics, Shanghai University, Shanghai 200444, China"},{"name":"School of Mathematics and Quantitative Economics, Shandong 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