{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:01:29Z","timestamp":1760151689230,"version":"build-2065373602"},"reference-count":41,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,8]],"date-time":"2022-04-08T00:00:00Z","timestamp":1649376000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12171278"],"award-info":[{"award-number":["12171278"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the present paper, an iterative algorithm is proposed for solving the generalized (P,Q)-reflexive solution group of a system of quaternion matrix equations \u2211l=1M(AlsXlBls+ClsXl\u02dcDls)=Fs,s=1,2,\u2026,N. A generalized (P,Q)-reflexive solution group, as well as the least Frobenius norm generalized (P,Q)-reflexive solution group, can be derived by choosing appropriate initial matrices, respectively. Moreover, the optimal approximate generalized (P,Q)-reflexive solution group to a given matrix group can be derived by computing the least Frobenius norm generalized (P,Q)-reflexive solution group of a reestablished system of matrix equations. Finally, some numerical examples are given to illustrate the effectiveness of the algorithm.<\/jats:p>","DOI":"10.3390\/sym14040776","type":"journal-article","created":{"date-parts":[[2022,4,10]],"date-time":"2022-04-10T06:02:54Z","timestamp":1649570574000},"page":"776","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Iterative Algorithm for the Generalized Reflexive Solution Group of a System of Quaternion Matrix Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1144-9834","authenticated-orcid":false,"given":"Jing","family":"Jiang","sequence":"first","affiliation":[{"name":"Department of Mathematics, QiLu Normal University, Jinan 250013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ning","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"140","DOI":"10.1137\/S0895479895288759","article-title":"Generalized reflexive matrices: Special properties and applications","volume":"19","author":"Chen","year":"1998","journal-title":"SIAM J. 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