{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:07:18Z","timestamp":1760267238830,"version":"3.40.5"},"reference-count":13,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"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":["10901056","11071079","11001167","11QA1402200","Y6110043"],"award-info":[{"award-number":["10901056","11071079","11001167","11QA1402200","Y6110043"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10901056","11071079","11001167","11QA1402200","Y6110043"],"award-info":[{"award-number":["10901056","11071079","11001167","11QA1402200","Y6110043"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["10901056","11071079","11001167","11QA1402200","Y6110043"],"award-info":[{"award-number":["10901056","11071079","11001167","11QA1402200","Y6110043"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Shanghai Science and Technology Commission","award":["10901056","11071079","11001167","11QA1402200","Y6110043"],"award-info":[{"award-number":["10901056","11071079","11001167","11QA1402200","Y6110043"]}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["10901056","11071079","11001167","11QA1402200","Y6110043"],"award-info":[{"award-number":["10901056","11071079","11001167","11QA1402200","Y6110043"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>We propose a new iterative method to find the bisymmetric minimum norm solution of a pair of consistent matrix equations<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msub><mml:mi>A<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><mml:mi>X<\/mml:mi><mml:msub><mml:mi>B<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><mml:mo>=<\/mml:mo><mml:msub><mml:mi>C<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><\/mml:mrow><\/mml:math>,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:msub><mml:mi>A<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><mml:mi>X<\/mml:mi><mml:msub><mml:mi>B<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><mml:mo>=<\/mml:mo><mml:msub><mml:mi>C<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><\/mml:mrow><\/mml:math>. The algorithm can obtain the bisymmetric solution with minimum Frobenius norm in finite iteration steps in the absence of round-off errors. Our algorithm is faster and more stable than Algorithm 2.1 by Cai et al. (2010).<\/jats:p>","DOI":"10.1155\/2013\/125687","type":"journal-article","created":{"date-parts":[[2013,3,12]],"date-time":"2013-03-12T17:07:37Z","timestamp":1363108057000},"page":"1-6","source":"Crossref","is-referenced-by-count":2,"title":["A New Method for the Bisymmetric Minimum Norm Solution of the Consistent Matrix Equations<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mi>A<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><mml:mi>X<\/mml:mi><mml:msub><mml:mi>B<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><mml:mo>=<\/mml:mo><mml:msub><mml:mi>C<\/mml:mi><mml:mn>1<\/mml:mn><\/mml:msub><\/mml:mrow><\/mml:math>,<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msub><mml:mi>A<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><mml:mi>X<\/mml:mi><mml:msub><mml:mi>B<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><mml:mo>=<\/mml:mo><mml:msub><mml:mi>C<\/mml:mi><mml:mn>2<\/mml:mn><\/mml:msub><\/mml:mrow><\/mml:math>"],"prefix":"10.1155","volume":"2013","author":[{"given":"Aijing","family":"Liu","sequence":"first","affiliation":[{"name":"Department of Mathematics, East China Normal University, Shanghai 200241, China"},{"name":"School of Mathematical Sciences, Qufu Normal University, Shandong 273165, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guoliang","family":"Chen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, East China Normal University, Shanghai 200241, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiangyun","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, East China Normal University, Shanghai 200241, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.12.026"},{"issue":"3","key":"6","first-page":"29","volume":"18","year":"2004","journal-title":"Journal of East China Shipbuilding Institute"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(00)00330-8"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(90)90377-O"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(84)90166-6"},{"issue":"4","key":"11","first-page":"404","volume":"38","year":"1976","journal-title":"Sankhy\u0101 A"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1137\/0131050"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1002\/nla.496"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.01.071"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1080\/00207160902722357"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2009.07.004"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511840371"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1137\/0711019"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/125687.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/125687.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/125687.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,30]],"date-time":"2016-07-30T06:07:00Z","timestamp":1469858820000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/125687\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":13,"alternative-id":["125687","125687"],"URL":"https:\/\/doi.org\/10.1155\/2013\/125687","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}