{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T10:44:49Z","timestamp":1776768289601,"version":"3.51.2"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2021,1,8]],"date-time":"2021-01-08T00:00:00Z","timestamp":1610064000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,8]],"date-time":"2021-01-08T00:00:00Z","timestamp":1610064000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J. Appl. Math. Comput."],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s12190-020-01486-6","type":"journal-article","created":{"date-parts":[[2021,1,8]],"date-time":"2021-01-08T15:03:19Z","timestamp":1610118199000},"page":"317-341","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Iterative solution to a class of complex matrix equations and its application in time-varying linear system"],"prefix":"10.1007","volume":"67","author":[{"given":"Wenli","family":"Wang","sequence":"first","affiliation":[]},{"given":"Caiqin","family":"Song","sequence":"additional","affiliation":[]},{"given":"Shipu","family":"Ji","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,1,8]]},"reference":[{"issue":"4","key":"1486_CR1","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1016\/j.camwa.2018.05.010","volume":"76","author":"M Hajarian","year":"2017","unstructured":"Hajarian, M.: Computing symmetric solutions of general Sylvester matrix equations via Lanczos version of biconjugate residual algorithm. Comput. Math. Appl. 76(4), 686\u2013700 (2017)","journal-title":"Comput. Math. Appl."},{"key":"1486_CR2","doi-asserted-by":"publisher","first-page":"755","DOI":"10.1007\/s40314-014-0138-7","volume":"34","author":"M Hajarian","year":"2018","unstructured":"Hajarian, M.: Developing CGNE algorithm for the periodic discrete-time generalized coupled Sylvester matrix equations. Comput. Appl. Math. 34, 755\u2013771 (2018)","journal-title":"Comput. Appl. Math."},{"key":"1486_CR3","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.camwa.2017.08.041","volume":"75","author":"CQ Lv","year":"2018","unstructured":"Lv, C.Q., Ma, C.F.: BCR method for solving generalized coupled Sylvester equations over centrosymmetric or anti-centrosymmetric matrix. Comput. Math. Appl. 75, 70\u201388 (2018)","journal-title":"Comput. Math. Appl."},{"key":"1486_CR4","doi-asserted-by":"publisher","first-page":"266","DOI":"10.13001\/1081-3810.3917","volume":"35","author":"ZH He","year":"2019","unstructured":"He, Z.H.: Pure PSVD approach to Sylvester-type quaternion matrix equations. Electron. J. Linear Algebra 35, 266\u2013284 (2019)","journal-title":"Electron. J. Linear Algebra"},{"key":"1486_CR5","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1016\/j.automatica.2018.07.021","volume":"97","author":"AG Wu","year":"2018","unstructured":"Wu, A.G., Sun, H.J., Zhang, Y.: An SOR implicit iterative algorithm for coupled Lyapunov equations. Automatica. 97, 38\u201347 (2018)","journal-title":"Automatica."},{"key":"1486_CR6","doi-asserted-by":"crossref","first-page":"410","DOI":"10.1016\/j.amc.2018.07.032","volume":"339","author":"AG Wu","year":"2018","unstructured":"Wu, A.G., Sun, H.J., Zhang, Y.: Two iterative algorithms for stochastic algebraic Riccati matrix equations. Appl. Math. Comput. 339, 410\u2013421 (2018)","journal-title":"Appl. Math. Comput."},{"key":"1486_CR7","doi-asserted-by":"publisher","first-page":"1260","DOI":"10.1016\/j.apm.2015.07.017","volume":"40","author":"N Huang","year":"2016","unstructured":"Huang, N., Ma, C.F.: Modified conjugate gradient method for obtaining the minimum-norm solution of the generalized coupled Sylvester-conjugate matrix equations. Appl. Math. Model. 40, 1260\u20131275 (2016)","journal-title":"Appl. Math. Model."},{"key":"1486_CR8","first-page":"547","volume":"17","author":"YG Peng","year":"2014","unstructured":"Peng, Y.G., Wang, X.: A finite iterative algorithm for solving the least-norm generalized (P, Q) reflexive solution of the matrix equations $$A_{i}XB_{i} n= C_{i}$$. J. Comput. Anal. Appl. 17, 547\u2013561 (2014)","journal-title":"J. Comput. Anal. Appl."},{"issue":"12","key":"1486_CR9","doi-asserted-by":"publisher","first-page":"1138","DOI":"10.1109\/TAC.1986.1104189","volume":"31","author":"LR Fletcher","year":"1986","unstructured":"Fletcher, L.R., Kuatslcy, J., Nichols, N.K.: Eigenstructure assignment in descriptor systems. IEEE Trans. Auto. Control 31(12), 1138\u20131141 (1986)","journal-title":"IEEE Trans. Auto. Control"},{"key":"1486_CR10","doi-asserted-by":"publisher","first-page":"1813","DOI":"10.1016\/j.automatica.2011.04.015","volume":"47","author":"B Zhou","year":"2011","unstructured":"Zhou, B., Zheng, W.X., Duan, G.R.: Stability and stabilization of discrete-time periodic linear systems with actuator saturation. Automatica 47, 1813\u20131820 (2011)","journal-title":"Automatica"},{"key":"1486_CR11","doi-asserted-by":"publisher","first-page":"2139","DOI":"10.1109\/TAC.2011.2181796","volume":"57","author":"B Zhou","year":"2012","unstructured":"Zhou, B., Duan, G.R.: Periodic Lyapunov equation based approaches to the stabilization of continuous-time periodic linear systems. IEEE Trans. Autom. Control 57, 2139\u20132146 (2012)","journal-title":"IEEE Trans. Autom. Control"},{"issue":"3","key":"1486_CR12","doi-asserted-by":"publisher","first-page":"1321","DOI":"10.1016\/j.jfranklin.2016.11.030","volume":"354","author":"F Ding","year":"2017","unstructured":"Ding, F., Wang, F.F., Xu, L., Wu, M.H.: Decomposition based least squares iterative identification algorithm for multivariate pseudo-linear ARMA systems using the data filtering. J. Frankl. Inst. 354(3), 1321\u20131339 (2017)","journal-title":"J. Frankl. Inst."},{"key":"1486_CR13","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1016\/j.automatica.2004.10.010","volume":"41","author":"F Ding","year":"2005","unstructured":"Ding, F., Chen, T.: Hierarchical gradient-based identification of multivariable discrete-time systems. Automatica 41, 315\u2013325 (2005)","journal-title":"Automatica"},{"key":"1486_CR14","doi-asserted-by":"publisher","first-page":"759","DOI":"10.1016\/j.cam.2008.06.014","volume":"224","author":"B Zhou","year":"2009","unstructured":"Zhou, B., Li, Z.Y., Duan, G.R., Wang, Y.: Weighted least squares solutions to general coupled Sylvester matrix equations. J. Comput. Appl. Math. 224, 759\u2013776 (2009)","journal-title":"J. Comput. Appl. Math."},{"key":"1486_CR15","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.sysconle.2004.06.008","volume":"54","author":"F Ding","year":"2005","unstructured":"Ding, F., Chen, T.: Iterative least squares solutions of coupled sylvester matrix equations. Syst. Control Lett. 54, 95\u2013107 (2005)","journal-title":"Syst. Control Lett."},{"key":"1486_CR16","doi-asserted-by":"publisher","first-page":"2269","DOI":"10.1137\/S0363012904441350","volume":"44","author":"F Ding","year":"2006","unstructured":"Ding, F., Chen, T.: On iterative solutions of general coupled matrix equations. SIAM J. Control Optim. 44, 2269\u20132284 (2006)","journal-title":"SIAM J. Control Optim."},{"key":"1486_CR17","doi-asserted-by":"publisher","first-page":"1216","DOI":"10.1109\/TAC.2005.852558","volume":"50","author":"F Ding","year":"2005","unstructured":"Ding, F., Chen, T.: Gradient based iterative algorithms for solving a class of matrix equations. IEEE Trans. Autom. Control 50, 1216\u20131221 (2005)","journal-title":"IEEE Trans. Autom. Control"},{"key":"1486_CR18","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1109\/TAC.2005.843856","volume":"50","author":"F Ding","year":"2005","unstructured":"Ding, F., Chen, T.: Hierarchical least squares identification methods for multivariable systems. IEEE Trans. Autom. Control 50, 397\u2013402 (2005)","journal-title":"IEEE Trans. Autom. Control"},{"key":"1486_CR19","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.amc.2007.07.040","volume":"197","author":"F Ding","year":"2008","unstructured":"Ding, F., Liu, P.X., Ding, J.: Iterative solutions of the generalized Sylvester matrix equations by using the hierarchical identification principle. Appl. Math. Comput. 197, 41\u201350 (2008)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"1486_CR20","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.amc.2010.05.029","volume":"217","author":"AG Wu","year":"2010","unstructured":"Wu, A.G., Zeng, X.L., Duan, G.R., Wu, W.J.: Iterative solutions to the extended Sylvester-conjugate matrix equatinos. Appl. Math. Comput. 217(1), 130\u2013142 (2010)","journal-title":"Appl. Math. Comput."},{"issue":"21","key":"1486_CR21","doi-asserted-by":"crossref","first-page":"8343","DOI":"10.1016\/j.amc.2011.02.113","volume":"217","author":"AG Wu","year":"2011","unstructured":"Wu, A.G., Lv, L.L., Duan, G.R.: Iterative algorithms for solving a class of complex conjugate and transpose matrix equations. Appl. Math. Comput. 217(21), 8343\u20138353 (2011)","journal-title":"Appl. Math. Comput."},{"issue":"1","key":"1486_CR22","doi-asserted-by":"publisher","first-page":"54","DOI":"10.1016\/j.camwa.2010.04.029","volume":"60","author":"AG Wu","year":"2010","unstructured":"Wu, A.G., Feng, G., Duan, G.R., Wu, W.J.: Iterative solutions to coupled Sylvester-conjugate matrix equations. Comput. Math. Appl. 60(1), 54\u201366 (2010)","journal-title":"Comput. Math. Appl."},{"key":"1486_CR23","doi-asserted-by":"publisher","first-page":"7585","DOI":"10.1016\/j.jfranklin.2017.09.005","volume":"354","author":"HM Zhang","year":"2017","unstructured":"Zhang, H.M., Yin, H.C.: New proof of the gradient-based iterative algorithm for a complex conjugate and transpose matrix equation. J. Frankl. Inst. 354, 7585\u20137603 (2017)","journal-title":"J. Frankl. Inst."},{"key":"1486_CR24","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1016\/j.jfranklin.2013.08.023","volume":"351","author":"HM Zhang","year":"2014","unstructured":"Zhang, H.M., Ding, F.: A property of the eigenvalues of the symmetric positive definite matrix and the iterative algorithm for coupled Sylvester matrix equations. J. Frankl. Inst. 351, 340\u2013357 (2014)","journal-title":"J. Frankl. Inst."},{"key":"1486_CR25","doi-asserted-by":"publisher","first-page":"2049","DOI":"10.1016\/j.camwa.2015.08.013","volume":"70","author":"HM Zhang","year":"2015","unstructured":"Zhang, H.M.: Reduced-rank gradient-based algorithms for generalized coupled Sylvester matrix equations and its applications. Comput. Math. Appl. 70, 2049\u20132062 (2015)","journal-title":"Comput. Math. Appl."},{"key":"1486_CR26","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1007\/s00006-019-0955-2","volume":"29","author":"ZH He","year":"2019","unstructured":"He, Z.H.: A system of coupled quaternion matrix equations with seven unknowns and its applications. Adv. Appl. Clifford Algebras 29, 38 (2019)","journal-title":"Adv. Appl. Clifford Algebras"},{"issue":"3","key":"1486_CR27","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1080\/00207160802123458","volume":"87","author":"B Zhou","year":"2010","unstructured":"Zhou, B., Lam, J., Duan, G.R.: Gradient-based maximal convergence rate iterative method for solving linear matrix equations. Int. J. Comput. Math. 87(3), 515\u2013527 (2010)","journal-title":"Int. J. Comput. Math."},{"key":"1486_CR28","doi-asserted-by":"publisher","first-page":"87","DOI":"10.1016\/j.aml.2015.08.017","volume":"52","author":"M Hajarian","year":"2016","unstructured":"Hajarian, M.: Solving the general Sylvester discrete-time periodic matrix equations via the gradient based iterative method. Appl. Math. Lett. 52, 87\u201395 (2016)","journal-title":"Appl. Math. Lett."},{"issue":"5","key":"1486_CR29","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/j.sysconle.2008.12.004","volume":"58","author":"B Zhou","year":"2009","unstructured":"Zhou, B., Duan, G.R., Li, Z.Y.: Gradient based iterative algorithm for solving coupled matrix equations. Syst. Control Lett. 58(5), 327\u2013333 (2009)","journal-title":"Syst. Control Lett."},{"issue":"8","key":"1486_CR30","doi-asserted-by":"publisher","first-page":"1580","DOI":"10.1080\/00207721.2010.549584","volume":"43","author":"M Dehghan","year":"2012","unstructured":"Dehghan, M., Hajarian, M.: The generalised Sylvester matrix equations over the generalised bisymmetric and skew-symmetric matrices. Int. J. Syst. Sci. 43(8), 1580\u20131590 (2012)","journal-title":"Int. J. Syst. Sci."},{"key":"1486_CR31","doi-asserted-by":"publisher","first-page":"533","DOI":"10.3846\/13926292.2016.1186119","volume":"21","author":"M Hajarian","year":"2016","unstructured":"Hajarian, M.: Gradient based iterative algorithm to solve general coupled discrete time periodic matrix equations over generalized reflexive matrices. Math. Model. Anal. 21, 533\u2013549 (2016)","journal-title":"Math. Model. Anal."},{"key":"1486_CR32","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/j.automatica.2017.09.008","volume":"87","author":"ZH He","year":"2018","unstructured":"He, Z.H., Wang, Q.W., Zhang, Y.: A system of quaternary coupled Sylvester-type real quaternion matrix equations. Automatica 87, 25\u201331 (2018)","journal-title":"Automatica"},{"key":"1486_CR33","doi-asserted-by":"publisher","first-page":"6","DOI":"10.1007\/s00006-018-0921-4","volume":"29","author":"ZH He","year":"2019","unstructured":"He, Z.H.: Structure, properties and applications of some simultaneous decompositions for quaternion matrices involving $$\\phi $$-skew-hermicity. Adv. Appl. Clifford Algebras 29, 6 (2019)","journal-title":"Adv. Appl. Clifford Algebras"},{"key":"1486_CR34","doi-asserted-by":"publisher","first-page":"1407","DOI":"10.1007\/s41980-019-00205-7","volume":"45","author":"ZH He","year":"2019","unstructured":"He, Z.H.: The general solution to a system of coupled Sylvester-type quaternion tensor equations involving $$\\eta $$-Hermicity. Bull. Iran. Math. Soc. 45, 1407\u20131430 (2019)","journal-title":"Bull. Iran. Math. Soc."},{"key":"1486_CR35","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1016\/j.cam.2018.09.001","volume":"349","author":"ZH He","year":"2019","unstructured":"He, Z.H., Wang, Q.W., Zhang, Y.: A simultaneous decomposition for seven matrices with applications. J. Comput. Appl. Math. 349, 93\u2013113 (2019)","journal-title":"J. Comput. Appl. Math."},{"key":"1486_CR36","doi-asserted-by":"publisher","first-page":"597","DOI":"10.1016\/j.camwa.2017.05.008","volume":"74","author":"XP Sheng","year":"2017","unstructured":"Sheng, X.P., Sun, W.W.: The relaxed gradient based iterative algorithm for solving matrix equations $$A_{i}XB_{i}=F_{i}$$. Comput. Math. Appl. 74, 597\u2013604 (2017)","journal-title":"Comput. Math. Appl."},{"key":"1486_CR37","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1002\/asjc.328","volume":"13","author":"Q Niu","year":"2011","unstructured":"Niu, Q., Wang, X., Lu, L.: A relaxed gradient based algorithm for solving Sylvester equations. Asian J. Control 13, 461\u2013464 (2011)","journal-title":"Asian J. Control"},{"key":"1486_CR38","doi-asserted-by":"publisher","first-page":"3168","DOI":"10.1016\/j.jfranklin.2018.02.014","volume":"355","author":"BH Huang","year":"2018","unstructured":"Huang, B.H., Ma, C.F.: The relaxed gradient-based iterative algorithms for a class of generalized coupled Sylvester-conjugate matrix equations. J. Frankl. Inst. 355, 3168\u20133195 (2018)","journal-title":"J. Frankl. Inst."},{"key":"1486_CR39","volume-title":"Matrix Analysis","author":"RA Horn","year":"1990","unstructured":"Horn, R.A., Johnson, C.R.: Matrix Analysis. Cambridge University Press, Cambridge (1990)"},{"key":"1486_CR40","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/S0024-3795(02)00633-X","volume":"367","author":"TS Jiang","year":"2003","unstructured":"Jiang, T.S., Wei, M.S.: On solutions of the matrix equations $$X-AXB=C$$ and $$X-A\\overline{X}B=C$$. Linear Algebra Appl. 367, 225\u2013233 (2003)","journal-title":"Linear Algebra Appl."}],"container-title":["Journal of Applied Mathematics and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01486-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s12190-020-01486-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s12190-020-01486-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,11]],"date-time":"2022-12-11T01:21:50Z","timestamp":1670721710000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s12190-020-01486-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,8]]},"references-count":40,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["1486"],"URL":"https:\/\/doi.org\/10.1007\/s12190-020-01486-6","relation":{},"ISSN":["1598-5865","1865-2085"],"issn-type":[{"value":"1598-5865","type":"print"},{"value":"1865-2085","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,8]]},"assertion":[{"value":"30 October 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 December 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 December 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 January 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}