{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,23]],"date-time":"2025-06-23T06:46:05Z","timestamp":1750661165010,"version":"3.37.3"},"reference-count":48,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11071041","2013J01006","JK2013060"],"award-info":[{"award-number":["11071041","2013J01006","JK2013060"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["11071041","2013J01006","JK2013060"],"award-info":[{"award-number":["11071041","2013J01006","JK2013060"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]},{"name":"University Special Fund Project of Fujian","award":["11071041","2013J01006","JK2013060"],"award-info":[{"award-number":["11071041","2013J01006","JK2013060"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>The iterative method is presented for obtaining the centrally symmetric (centrally antisymmetric) matrix pair<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mi>X<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>Y<\/mml:mi><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>solutions of the generalized coupled Sylvester-conjugate matrix equations<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:msub><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mi>X<\/mml:mi><mml:mo>+<\/mml:mo><mml:msub><mml:mrow><mml:mi>B<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mi>Y<\/mml:mi><mml:mo>=<\/mml:mo><mml:msub><mml:mrow><mml:mi>D<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mover accent=\"false\"><mml:mrow><mml:mi>X<\/mml:mi><\/mml:mrow><mml:mo>\u00af<\/mml:mo><\/mml:mover><mml:msub><mml:mrow><mml:mi>E<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>+<\/mml:mo><mml:msub><mml:mrow><mml:mi>F<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">1<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:msub><mml:mrow><mml:mi>A<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mi>Y<\/mml:mi><mml:mo>+<\/mml:mo><mml:msub><mml:mrow><mml:mi>B<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mi>X<\/mml:mi><mml:mo>=<\/mml:mo><mml:msub><mml:mrow><mml:mi>D<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mover accent=\"false\"><mml:mrow><mml:mi>Y<\/mml:mi><\/mml:mrow><mml:mo>\u00af<\/mml:mo><\/mml:mover><mml:msub><mml:mrow><mml:mi>E<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>+<\/mml:mo><mml:msub><mml:mrow><mml:mi>F<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn mathvariant=\"normal\">2<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:math>. On the condition that the coupled matrix equations are consistent, we show that the solution pair<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mo stretchy=\"false\">(<\/mml:mo><mml:msup><mml:mrow><mml:mi>X<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">*<\/mml:mi><\/mml:mrow><\/mml:msup><mml:mo>,<\/mml:mo><mml:msup><mml:mrow><mml:mi>Y<\/mml:mi><\/mml:mrow><mml:mrow><mml:mi mathvariant=\"normal\">*<\/mml:mi><\/mml:mrow><\/mml:msup><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:math>can be obtained within finite iterative steps in the absence of round-off error for any initial value given centrally symmetric (centrally antisymmetric) matrix. Moreover, by choosing appropriate initial value, we can get the least Frobenius norm solution for the new generalized coupled Sylvester-conjugate linear matrix equations. Finally, some numerical examples are given to illustrate that the proposed iterative method is quite efficient.<\/jats:p>","DOI":"10.1155\/2014\/515816","type":"journal-article","created":{"date-parts":[[2014,7,8]],"date-time":"2014-07-08T18:13:15Z","timestamp":1404843195000},"page":"1-17","source":"Crossref","is-referenced-by-count":4,"title":["Iterative Methods to Solve the Generalized Coupled Sylvester-Conjugate Matrix Equations for Obtaining the Centrally Symmetric (Centrally Antisymmetric) Matrix Solutions"],"prefix":"10.1155","volume":"2014","author":[{"given":"Yajun","family":"Xie","sequence":"first","affiliation":[{"name":"School of Mathematics and Computer Science, Fujian Normal University, Fuzhou 350007, China"},{"name":"College of Fujian Jiangxia, Fuzhou 350108, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Changfeng","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Mathematics and Computer Science, Fujian Normal University, 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